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PUBLISHERS OF bOOKS F O Fl.^ 

Coal Age ^ Electric Railway Journal 
Electrical World ^ Engineering News -Record 
American Machinist v Ingenieria Intemacional 
Engineering 8 Mining Journal ^ Power 
Chemical d> Metallurgical Engineering 
Electrical Merchandising 



ENGINEERING EDUCATION SERIES 



ADVANCED SHOP DRAWING 



PREPARED IX THE 

EXTENSION DIVISION OF 
THE UNIYEESITY OF WISCONSIN 



BY 

VIXCEXT C. GEORGE, B. S. 

IXSTRUCTOR IX MECHANICAL ENGINEERING 
THE UXn'ERSlTY OF WISCONSIN 



First Edition 



McGRAW-HILL BOOK COMPANY, Ixc. 

NEW YORK: 370 SEVENTH AVENUE 

LONDON: 6 & 8 BOUVERIE ST., E. C. 4 

1920 



s'^ 






Copyright, 1920, by the 
McGraw-Hill Book Company, Inc. 



THK MAPLE PRESS YORK PA 



QEC -8 ld20 
©Ci.AG04509 



PREFACE 

The contents of this book have been laid out with the ob- 
ject in view of enabhng any one who has had some prehminary 
training in Mechanical Drawing and in the use of drawing in- 
struments, to gain a practical knowledge of drafting as applied 
to various lines of engineering. The text material and problems 
have been so arranged that they should not be difficult for 
the student who has had sufficient practice in drawing to have 
become familiar with the principles of orthographic projection 
and the use of drawing instruments. 

Emphasis has been laid on drafting as applied to such special 
subjects as Pictorial Representation, Patent Office Drawings, 
Electrical Drawing, Piping Layouts, Structural Drawing, and 
Sheet Metal Work. These chapters are not elaborate but are 
designed to give the draftsman a working knowledge of these 
lines. 

The author wishes to express his appreciation to Professor 
Ben G. Elliott of the Department of Mechanical Engineering of 
the Extension Division, University of Wisconsin, for his many 
helpful suggestions and criticisms given during the preparation 
of this book, and to Professor H. D. Orth, Department of En- 
gineering Drawing, University of Wisconsin, for his helpful criti- 
cism of the completed manuscript. Acknowledgment is due also 
to the C. F. Pease Company of Chicago, for the use of some of 
their cuts of blue printing machines. 

. V. C. George. 
The University of Wisconsin, 
Madison, Wisconsin. 
October 1, 1920. 



CONTENTS 



CHAPTER I 
WoRKii<jG Drawings 



Art 



Page 

1. Assembly Drawings 1 

2. Detail Drawings ^ 

3. Scale 8 

4. Legend ^ 

5. Title 10 

6. Tracing • H 

7. Blue Printing 12 

8. Vandykes 13 

Problems 14 

CHAPTER II 

Gearing 

9. Spur Gears 15 

10. Pitch Circles • • • 1^ 

11. Pitch Diameter 17 

12. Pitch •. 17 

13. Diametral Pitch 17 

14. Circular Pitch 18 

15. Addendum Circle 19 

16. Dedendum Circle 21 

17. Root or Clearance Circle 21 

18. Tables of Tooth Parts 22 

19. Velocity Ratio 23 

20. Special Gears 25 

21. Gear Drawings 25 

Problems 30 

CHAPTER III 

Gearing (Bevel, Worm, and Special Gears) 

22. Bevel Gears 31 

23. Bevel Gear Layout 31 

24. Worm and Worm Wheel ' 36 

25. Shop Drawing of Worm and Worm Wheel 38 

26. Special Gears • 39 

Problems 46 

vii 



viii CONTENTS 

CHAPTER IV 

Isometric, Cabinet, and Shaded Drawings 
Akt. Page 

27. Isometric Drawing 47 

28. Cabinet Drawing 53 

29. Shaded Drawings 57 

30. Shade Lines 57 

31. Line Shading 60 

32. Special Cases 62 

Problems 66 

CHAPTER V 

Patent Office Drawings 

33. Application 67 

34. Examination 68 

35. Drawing 68 

Problem 74 

CHAPTER VI 

Structural Drawing 

36. Structural Drawing 75 

37. Estimating Department 75 

38. Drafting Department 75 

39. Examples of Structural Drawings 79 

40. Templet Shop 83 

41. Beam Shop 84 

42. Assembling Shop 84 

43. Yard * 84 

Problem 84 

CHAPTER VII 

Electrical Drawing 

44. Electrical Drawing 86 

45. Symbols 86 

46. Wire Size 87 

47. Bell Circuits 87 

48. Two-wire Circuits 89 

49. Three-wire Circuits 90 

50. Wiring Diagrams 93 

Problem 97 

CHAPTER VIII 

Plans for Pipe Systems 

51. Pipe 100 

52. Pipe Sizes 100 

53. Pipe Thread 101 



CONTENTS ix 

Art. Page 

54. Fittings 102 

55. Piping Symbols 103 

56. Piping Drawings 104 

Problem 113 

CHAPTER IX 

Sheet Metal Work 

57. Fundamental Principles 114 

58. Developments 115 

59. Curves and Circles 115 

60. Intersections 116 

61. Materials Used 118 

62. Seams 121 

63. Prism Intersection 123 

64. Prism Developments 124 

Problems 129 

CHAPTER X 

Sheet Metal Work (Continued) 

65. Triangulation 132 

66. Development by Triangulation 132 

67. Elbows 136 

68. Allowance for Thickness of Metal 139 

Problems 142 

Index 145 



ADVANCED SHOP DRAWING 



CHAPTER I 
WORKING DRAWINGS 

1. Assembly Drawings. — There are several types of assembly 
drawings. Among these are Outline or Setting Drawings, Dia- 
gram Drawings, Assembly Working Drawings, Part Assembly 
Drawings, Erection Drawings, and General Assembly Drawings. 

An outline assembly drawing shows the machine only in out- 
line with no attempt at details. Center distances and over-all 
dimensions are given. Such an assembly is shown in Fig. 1. 
An outline assembly drawing is used both for catalog illustra- 
tions and for showing prospective customers an outline of the 
machine. In such cases only the general appearance of the 
machine is necessary. 

A diagram drawing, Fig. 2, gives either a sectional or an external 
view of the whole machine. In this kind of an assembly all the 
parts are either numbered or named. A list of parts is included 
on the drawing. Pattern numbers are sometimes given. 

An assembly working drawing is used when only a few ma- 
chines are to be made. Each part is fully dimensioned. This 
makes it possible for the mechanic to build the machine from 
the assembly drawing instead of having to refer to several detail 
sheets. By this method a great deal of time is saved in the draft- 
ing room, since each detail does not have to be drawn separately. 

Part assembly drawings are those in which only a few parts of 
the machine are shown. In such cases these parts should be 
shown in their relation to the whole machine and also to each 
other. An assembly drawing is made of these parts, each part 
being fully dimensioned. Complete dimensioning does away 
with the necessity of drawing details. 

Erection drawings are those used in the erection of a machine. 
Each part is numbered or named so that it may be easily identi- 
fied. These drawings give the exact location of each part and 
the proper order of procedure in the erection of the machine. 

1 



ADVANCED SHOP DRAWING 




WORKING DRAWINGS 3 

General assembly drawings are used in machine design. 
When the design of a machine is taken up in a drafting office, the 
chief engineer or a senior draftsman first makes the preliminary 
sketches or a general assembly drawing of it. This general 
assembly drawing shows all the general dimensions which limit 
the working strength or working capacity of the machine and 
which show the general relation of the various parts to each 
other in the assembled machine. 




Fig. 2. — Diagram assembly of Kempsmith dividing head. 

This general assembly drawing is then turned over to a junior 
draftsman or a ''detailer" who makes complete detail drawings 
of each part of the machine from which the mechanics make the 
various parts. Such plates of details are called detail sheets. 
All these pencil drawings are then turned over to the ''tracer" 
who makes the tracings from which the blue prints are made. 
In small offices, all of these operations may be performed b}^ the 
same man. The tracings are then checked over by a competent 
draftsman. 



4 ADVANCED SHOP DRAWING 

An assembly drawing of a tailstock for a 12-inch lathe is shown 
in Fig. 3. The title appears at the top of the plate as is the 
practice of some concerns. In the upper right-hand corner of 
the plate a ''Bill of Material" is found. In some cases this bill 
of material is shown on a separate sheet. An assembly drawing 
such as this would be handed to a detailer or junior draftsman 
to make the detail drawings. 

The Acme threads on the screw are usually drawn with a 30° 
angle between them instead of the 29° angle which is actually 
between the threads. The thread outlines on each side of the 
screw are then connected with straight lines. An Acme thread 
is shown in Fig. 4. 

The center has a taper of J^'' per foot. This means that if it 
were 1' long and 3^^'' m diameter at one end, the diameter at the 
other end would be zero. In this case, however, the diameter of 
the small end is ^Me"; the diameter at the large end, if it were 
1' long, would be ^Me'' + }^" = iMe"- ^^ order to show 
the correct taper, it is necessary to draw two light pencil lines 
along an axis V long. These two lines should be ^Me'' apart 
at one end and l^i^" apart at the other end. The length of the 
center should be laid off from the small end. 

A detail drawing should show the diameter of the large end 
rather than the diameter of the small end, because it is easy for 
the machinist to measure the diameter of the large end with 
a micrometer. Showing the diameter of the large end together 
with the length of the center makes it unnecessary to show the 
diameter of the small end. 

A feather key is a key used to fasten two machine parts 
together, allowing one to slide on the other, but not allowing one 
to turn without turning the other. The feather key in this case 
is fastened into the body of the tailstock, and fits loosely into a 
keyway in the spindle so that the spindle can move back and 
forth, but cannot turn. The lug on one end of the key is circular 
and Ke" ii^ diameter. In order to drill the hole in the bottom of 
the keyway in the body for the lug to fit into, it is necessary to 
drill down through the top of the body. This hole in the top 
must afterwards be plugged so that it will not show. 

In the case of a small machine it is the usual practice to place 
the general assembly in the upper left-hand corner of the 
plate, the rest of the plate being given over to the drawings 
of the details. In the case of a large machine requiring 



WORKING DRAWINGS 



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several plates of details the assembly is generally shown on a 
separate plate. 

2. Detail Drawings. — A detail drawing is one which shows each 
part of the machine separately. The parts are fully dimensioned 
and enough views of each given so that the mechanic can make 
the piece without other instructions. If necessary, explanatory 
notes are added to the drawing to make the construction clear. 

The details are sometimes drawn on the plates in the logical 
arrangement in which they occur in the machine; that is, adjacent 
parts in the machine are drawn adjacent to each other on the 
detail sheets. Sometimes the details of units which are to be 




V Thread 




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Acme Thread Wor m Thread (B 8:5 5td.) WhitworthThread 

Fig. 4. — Standard thread outlines. 

made and perhaps assembled in one part of the shop are grouped 
together on the detail sheets. In other cases, it may be convenient 
to group together the details of similar parts which are to be made 
by the same mechanic or department. In one group may be 
found all the details of the shafts required; in another group all 
the gears; in a third group all the gear guards, etc. The choice 
of an}^ of these methods will be determined largely by the local 
conditions governing the manufacture of the machine. 

Figure 5 shows the details of the crank end of a connecting 
rod. This is a simple bolted strap end which resists the tension 
of the rod by the shearing strength of the bolts and the friction 
set up between the stub end and the strap by the tightening of 
the bolts. It is a very firm and solid construction. Some such 
open end type of construction is always necessary on a center 
crank engine. 



WORKING DRAWINGS 




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In assembling this end, the boxes are placed over the crank pin, 
the strap placed around the boxes, and the wedge secured in 
position by means of the cap screws. The stub end is next moved 
into position between the jaws of the strap, and is secured by the 
bolts. 

On account of the heavy service for which the rod is designed, 
there is no allowance made for play between the boxes. The 
boxes are made of cast iron, babbitted, with flanges to prevent 
lateral movement. The babbitt, which forms the rubbing sur- 
face, is an anti-friction metal, sufficiently fusible to be melted 
in a common ladle. Its use is very desirable because of its prop- 
erty of forming a perfect bearing easily without the necessity 
of reboring. The boxes are held in position by a wedge which is 
raised and lowered by means of two cap screws passing through 
the strap and tapped into the wedge. 

3. Scale. — It is generally necessary to make mechanical draw- 
ings to some convenient scale. The scales to which the several 
details are drawn should be so chosen that the space allotted to 
each detail will bear some reasonable proportion to the space 
allotted to the other details. In other words, a comparatively 
small and insignificant part should not be drawn to a large scale 
and a larger and much more important part to a much reduced 
scale. If, however, a certain small part is highly important and 
intricate in design, it may be advisable to draw it to a large scale 
in order to show it clearly and to emphasize the fact that it should 
be accurately made. The space given to each detail should he in 
proportion to its importance and size, thus giving the plate a proper 
balance. 

4. Legend. — Beneath each detail there should appear a title 
or ''legend. " This legend gives the name of the part, the number 
required for one machine, the material of which it is to be made, 
and whatever finish, if any, is required. 

A legend may appear something like this: 

Face Plate 
1 — Required Cast Iron 
Scale ?," = V 
or 

Stuffing Box 
Gland 
2 — Required Brass 
Scale 6'' = 1' 



WORKING DRAWINGS 



9 



FIRST USED ON. 



MATERIAL 



MAT SPEC. 



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FINISH 



ALLOWABLE VARIATION ON PIMENStONS LOCATING FINISHED 
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Fig. 6. — Standard titles. 



10 ADVANCED SHOP DRAWING 

The legend together with the views of the detail and all di- 
mensions gives all the necessary information concerning the part. 
5. Title. — The title for the plate appears in the lower right- 
hand corner in every case. If the plate contains both assembly 
and details, the title for the plate may appear as follows : 

Follow Rest 

FOR 

12" Engine Lathe 

If the plate contains the assembly drawing only, the title of the 
plate will appear thus: 

Follow Rest 

FOR 

12'' Engine Lathe 
Assembly Drawing 

If the plate contains only the drawings of details, the title of the 
plate will appear thus: 

Details of Follow Rest 

FOR 

12'' Engine Lathe 

Nearly every manufacturing concern has its own standard 
title. A few of these are shown in Fig. 6. The name of the 
company and the spaces for the date, the check marks, the drafts- 
man's initials, etc. are stamped on every tracing made by that 



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Fig. 7. — Record strip title. 

company. This gives a standard title. A space is left for the 
name of the drawing, to be lettered in by the draftsman. The 
draftsman's name should appear in writing in the corner of every 
plate. The name should not be lettered in. In Fig. 7 is shown 
a record strip title. The spaces in the center are left for records 
of changes which may be made from time to time on the original 
tracing. Spaces are left in each case for the particular informa- 



WORKING DRAWINGS 



11 



tion needed by the company. If a bill of material is to be added, 
it is usually placed just above the title corner or in the upper 
right-hand corner as shown in Fig. 8. 



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Fig. 8.— Title with bill of material. 

6. Tracing.— The usual order of procedure in tracing is as 
follows : 

1. Center lines. 

2. Small circles and arcs of circles. 

3. Large circles. 

4. Straight object lines. 

5. Extension and dimension lines. 

Two guide lines should be drawn in light pencil for lettering. 
These should be erased after the tracing is finished. 

Tracing cloth has a dull side and a glossy side. Either side 
may be used to work on, but most draftsmen prefer the dull side 
as it will take a pencil mark. Before any lines are inked in, the 
cloth should be dusted with chalk dust or talcum powder to 



12 ADVANCED SHOP DRAWING 

remove the oily preservative which covers the surface. This oil, 
if allowed to remain on the cloth, will prevent the cloth from taking 
the ink properly and ragged lines will result. Some drafting 
offices use tracing paper instead of cloth because it is less expen- 
sive. It is not so durable, however. Sometimes pencil draw- 
ings are made on transparent paper and blue prints made directly 
from these, thus saving the expense of tracing. This is usually 
done when a blue print is needed in less time than the slower 
process of tracing permits. These drawings must be made with 
a soft pencil to insure heavy black lines. If the lines are not 
fairly heavy, the resulting blue print will appear weak. 

7. Blue Printing. — Blue printing is done on sensitized paper 
by exposing it either to sunlight or to artificial light. Before 
the paper is exposed it has a yellow color. On exposure to light 
the paper turns blue with a bronze tint. When blue prints are 
made, the light is allowed to shine through the tracing on to the 
paper. Since the paper is sensitized only on one side, care must 
be taken to expose the yellow side to the light. The inked lines 
on the tracing do not allow the light to pass through and thus the 
drawing is printed. When the paper has been properly exposed, 
it is removed from the printing frame and washed in clean water. 
The water ''fixes" the print and brings out the details clearly. 
Wherever the light strikes, the paper turns blue, but where the 
lines on the tracing protect it, the paper remains as it was. 

Some experience is necessary in order to expose the paper 
properly. Usually the paper is tested by exposing several small 
pieces until the proper degree of exposure is determined. This 
saves wasting several full-sized prints. In case the paper is 
under-exposed, the print is ruined, but if it is over-exposed it 
may be placed in a water bath which contains a solution of bichro- 
mate of potassium. This will intensify the blue, leaving the 
white lines more distinct. The print should be thoroughly 
washed in clear water after intensifying. Blue print clotL is 
used in some cases where a durable print is desired. 

There are several machines on the market for making blue 
prints. Figure 9 shows an upright electric machine. An electric 
arc lamp furnishes the light. The tracing is placed on the 
glass cylinder with the paper next to the tracing. The canvas 
roll holds the tracing andfthe paper securely in place while the 
printing is being done. The electric arc travels from the top to 
the bottom of the machine at a rate of speed which may be 




Fig. 9. — Upright electric blue print machine. 

{Facing page 12.) 




Fig. 10. — Sunlight blue print machine. 




Fig. 11. — C. F. Pease continuous blue print machine. 



WORKING DRAWINGS 13 

varied, depending on how long the operator wishes to expose 
the print. 

A sunhght machine is shown in Fig. 10. This machine works 
on a frame which is usually attached to a window sill. After 
the paper and tracings have been adjusted, the frame is placed 
outside the window in the sunlight. The advantage of this 
machine is the low first cost and small running expense. The 
disadvantage is that it is absolutely dependent on sunshine. 
The intensity of the light varies so much throughout the day 
and from day to day that it is difficult to know how to expose the 
paper properly. 

Some electric machines work continuously. Such a machine 
is shown in Fig. 11. It is so arranged that the paper is fed in 
from a roll. The paper passes slowly through the machine and 
directly through the special washing and drying device which 
is attached. Such machines are used in large offices where great 
quantities of prints are turned out each day. 

Black Prints. — Black prints are similar to blue prints except 
that black lines are produced on a white background. This 
paper is not used to the extent that blue print paper is used. 

Mounting Prints. — -Prints used in the shops are necessarily 
handled a great deal and unless they are protected will soon 
become spoiled. They may be protected by mounting them on 
cardboard or, as is done in some cases, on sheet iron. When 
mounted, they are usually covered with a coat of shellac which 
prevents them from becoming dirty and unreadable. They may 
be rendered waterproof by treating them with a solution of one 
part paraffin and three parts gasoline. They should be allowed 
to remain in this solution for a few minutes and then be wiped off. 
If the solution dries on them, they will be covered with paraffin. 
The paper will soak up enough paraffin to make it waterproof. 

8. Vandykes. — In printing from a tracing, only one print can 
be made at a time. It is sometimes necessary on large orders 
to make several prints at the same time. , In such cases instead of 
making more than one tracing, which is expensive, Vandyke 
copies are made. Vandyke paper or cloth is so treated that on 
exposure to light it turns dark and becomes opaque. Wherever 
the light does not strike, it becomes transparent. The same 
tracing may be used to print several Vandykes. After Vandykes 
are printed, they are washed in clear water and then placed in a 
fixing solution which renders them impervious to light. The 



14 ADVANCED SHOP DRAWING 

fixing solution is made up from the fixing salt which is usually 
sent with each roll of Vandyke paper. Full directions for making 
the solution accompany each package of salt. 

After fixing, the Vandykes are washed again and allowed to 
dry. These Vandykes are used instead of tracings for making 
prints. Before printing, the Vandykes are usually wiped with a 
cloth dampened in a mixture of gasoline and white oil. This 
makes them clearer and more transparent, and also removes any 
dirt which may have collected on them. The prints obtained 
are white prints, however, since only the lines of the drawing are 
transparent. On white prints, the lines are blue on a white 
background. 

Problem 1 
Make an assemblj^ drawing of the crank end details shown in Fig. 5. 
Use a 12" X 18" sheet with the 18" dimension horizontal. The drawing 
should be made to a 3" scale (3" = 1')- Draw the views and sections 
indicated in the small sketch. 

Problem 2 

Make full size detail drawings of the clamp bolt, clamj) bolt nut, clamp bolt 
washer, adjusting screws, and binder stiids for the 12" lathe tailstock 
shown in Fig. 3. Use the standard 12" X 18" sheet of drawing paper 
placed horizontally on the drawing board for these details. The legend 
for each part should be put under the drawing of it, as explained in 
Article 4. 

In the plate title in the lower right-hand corner put 

Details of 12" Tailstock 

together with the scale, date, etc. 

Problem 3 

Make a full size detail drawing of the binder plugs, binder washer, binder 
handle, spindle crank, and spindle crank handle of the 12" tailstock. The 
directions given previously should be followed. 

Problem 4 

Make a full size drawing of the spindle, spindle screw, spindle screw nut, 

spindle screw washer, center, and feather key of the 12" tailstock shown in 
Fig. 3. 

Decide which size drawing paper to use and arrange the parts on the sheet 
so that they will be well balanced. 

Problem 5 

Make a half size drawing of the base and clamp of the 12" tailstock, 
showing enough views to make them entirely clear. 

Problem 6 

Make a half size drawing of the tailstock body and cap of the 12" tail- 
stock, showing enough views and sections to make them entirely clear. 



CHAPTER II 



GEARING 



9. Spur Gears. — Spur gears are the most common type of 
gears and are used for power transmission between parallel 
shafts. The gears of Fig. 12 would be called a pair of spur gears, 
or a spur gear and pinion, the smaller one being the pinion. 
Figure 13 shows the names of the different parts of a gear. 
Figure 14 shows two cylinders rolling together without slipping. 
In order to transmit more power than can be transmitted by the 




Fig. 12. — Spur gear and pinion. 

smooth surfaces, projections may be put on B parallel to the 
axis, and corresponding recesses on^. If, now, it is considered 
that A is provided with similar projections and B with similar 
recesses, one can see clearly the direct transition from the rolling 
cyHnders of Fig. 14 to the toothed cylinders of Fig. 15 and then 
to the spur gears of Fig. 12. 

10. Pitch Circles. — -The pitch circles of spur gears are the same 
as the circumferences of the imaginary contact cylinders such as 
shown in Fig. 15. It is from these pitch circles that all gearing 
calculations are made. 

15 



16 



ADVANCED SHOP DRAWING 



ROOT CIRCLE 
DEDENOUM CIRCLE 
PITCH CIRCLE 
ADDENDUM CIRCLE 




Fig. 13. — Gear parts. 




Fig. 14. — Friction cylinders. 




Fig. 15. — Toothed cylinders. 



GEARING 17 

11. Pitch Diameter. — The pitch diameter of a gear is the diameter 
of its pitch circle. This is the diameter used in nearly all gear 
calculations. 

12. Pitch. — Pitch is a word used to designate the size of teeth 
on a gear. There are two kinds of pitch, diametral and circular. 
The diametral pitch system is the one generally used. 

13. Diametral Pitch. — ^Diametral pitch is the number of teeth 
on a gear for each inch of diameter of its pitch circle. If there 
are 32 teeth on a gear, and the diameter of its pitch circle is 
4'', there are ^% or 8 teeth per inch of diameter of the p'itch 
circle. The diametral pitch is, consequently, 8. 

To Find the Pitch Diameter. — Having given the number of teeth 
and the diametral pitch, divide the number of teeth by the 
diametral pitch. 

Example. — What is the pitch diameter of a gear having 66 
teeth and of 12 diametral pitch? 

Let P = diametral pitch. 



Then 



D = pitch diameter 
N = number of teeth 



D = 



N 

P 

66 



i) = j^ or 5M" (1) 

To Find the Diametral Pitch. — Having given the pitch diameter 
and the number of teeth, divide the number of teeth by the pitch 
diameter. 

Example. — What is the diametral pitch of a gear having 48 
teeth and a pitch diameter of 6''? 

P = ^ 
D 

48 
P = ^ or 8 (2) 

To Find the Number of Teeth. — Having given the diametral pitch 
and the pitch diameter, multiply the pitch diameter by the dia- 
metral pitch. 

Example. — How many teeth in a gear of 4^^" pitch diameter 
and 8 pitch? 

N = P X D 

iV = 4M X 8 or 37 (3) 



18 ADVANCED SHOP DRAWING 

Consequently, it is seen that, having given any two of the three 
terms — pitch diameter, diametral pitch and number of teeth, — the 
third can be readily found. 

14. Circular Pitch. — Circular pitch is the distance between 
similar points of adjoining teeth measured on the pitch circle 
as indicated in Fig. 13. It is the distance from the center of one 
tooth to the center of the next, or from the side of one tooth to 
the corresponding side of the next, the distance in both cases 
being measured around on the arc of the pitch circle, as in Fig. 
13, and not straight across on the chord. 

In solving for the pitch diameter, circular pitch, or number of 
teeth, by the circular pitch system, it is necessary to make use 
of the constant 3.1416. This constant is designated by the 
Greek letter w (pronounced as if spelled "pie ") . The pitch diam- 
eter, the circular pitch, or the number of teeth can be found if 
two of these are known. 

To Find the Pitch Diameter. — Having given the number of 
teeth and the circular pitch, multiply the circular pitch by 
the number of teeth and divide by tt. 

Example. — What is the pitch diameter of a gear which has 48 
teeth and ^" circular pitch? 

Let P' = circular pitch 
D = pitch diameter 
N = number of teeth 
7r= 3.1416 

^ ^ P' XN 

To Find the Circular Pitch. — Having given the pitch diameter 
and the number of teeth, multiply the pitch diameter by r (which 
gives the circumference of the pitch circle), and divide this cir- 
cumference by the number of teeth. 

Example. — What is the circular pitch of a gear having 36 teeth 
and a pitch diameter of d"? 

N 

P' = ^iMl|->l^ or 0.4363" (5) 

36 



GEARING 19 

To Find the Number of Teeth. — Having given the circular pitch 
and the pitch diameter, multiply the pitch diameter by w and 
divide by the circular pitch. 

Example. — What is the number of teeth in a gear having a 
circular pitch of 1}^'' and a pitch diameter of 7J-^''? 

N = Zi?^|:AM6 ^^. ^g 22 teeth (6) 

1.25 

Since there cannot be a fractional part of a tooth, it will be 
necessary to change either the pitch diameter or the pitch so as 
to have a whole number of teeth. The number of teeth may 
be assumed to be 18 and the circular pitch IJi". The pitch 
diameter to correspond may be found by Formula (4) : 

j^ 1.25 X 18 

The circular pitch system has the disadvantage that either the 
pitch diameter or the circular pitch will always be an inconvenient 
fraction, due to the fact that tt (3.1416) is always used in making 
the calculations. It is rapidly becoming obsolete. It is used, 
however, by pattern makers in spacing the teeth on patterns for 
cast gears. 

There is a definite relation between circular pitch and diam- 
etral pitch. Having given the circular pitch, one can find the 
equivalent diametral pitch, or having given the diametral pitch, 
one can find the equivalent circular pitch. 

ttD 
N = P XD or ~ 



PXD = 
P = 



ttD 
P' 



TT 
P XP'= TT 



This means that diametral pitch X circular pitch = tt 
Also P' ='^ 

15. Addendum Circle. — The addendum circle is the circle 
bounding the ends of the teeth. By referring to Table 1, Col- 



20 



ADVANCED SHOP DRAWING 



umn 4, it will be seen that, for length of standard teeth, the radius 
of the addendum circle is greater than that of the pitch circle 

by an amount „, so that its diameter is greater than that of the 

2 

pitch circle by an amount of p. Hence, to find the outside 

Table 1. — Gear Wheels 
Table of Tooth Parts — ^Diametral Pitch in First Column 



Diam- 
etral 
pitch 
P 


Circular 

pitch 

P" 


Thickness 

of tooth on 

pitch line 

t 


Addendum 
or 1" 

s 


Working 

depth of 

tooth 

D" 


Depth of 

space below 

pitch line 

s+f 


Whole depth 
of tooth 
D" +f 


K 


6.2832 


3.1416 


2.0000 


4.0000 


2.3142 


4.3142 


M 


4.1888 


2.0944 


1.3333 


2.6666 


1 . 5428 


2.8761 


1 


3.1416 


1 . 5708 


1 . 0000 


2.0000 


1.1571 


2.1571 


IK 


2.5133 


1.2566 


. 8000 


1 . 6000 


0.9257 


1.7257 


13-^ 


2 . 0944 


1 . 0472 


0.6666 


1.3333 


0.7714 


1.4381 


m 


1 . 7952 


0.8976 


0.5714 


1.1429 


0.6612 


1.2326 


2 


1 . 5708 


0.7854 


0.5000 


1.0000 


0.5785 


1.0785 


2H 


1 . 3963 


0.6981 


•0.4444 


0.8888 


0.5143 


0.9587 


2>i 


1.2566 


0.6283 


. 4000 


0.8000 


0.4628 


0.8628 


2H 


1 . 1424 


0.5712 


0.3636 


0.7273 


0.4208 


0.7844 


3 


1.0472 


0.5236 


0.3333 


0.6666 


0.3857 


0.7190 


3>^ 


0.8976 


0.4488 


0.2857 


0.5714 


0.3306 


0.6163 


4 


0.7854 


0.3927 


0.2500 


. 5000 


0.2893 


0.5393 


5 


0.6283 


0.3142 


0.2000 


0.4000 


0.2314 


0.4314 


6 


0.5236 


0.2618 


0.1666 


0.3333 


0.1928 


0.3595 


7 


0.4488 


0.2244 


0.1429 


0.2857 


0.1653 


0.3081 


8 


0.3927 


0.1963 


0.1250 


0.2500 


0.1446 


0.2696 


9 


0.3491 


0.1745 


0.1111 


0.2222 


0.1286 


0.2397 


10 


0.3142 


0.1571 


. 1000 


. 2000 


0.1157 


0.2157 


11 


0.2856 


0.1428 


0.0909 


0.1818 


0.1052 


0.1961 


12 


0.2618 


0.1309 


0.0833 


0.1666 


. 0964 


0.1798 


13 


0.2417 


0.1208 


0.0769 


0.1538 


. 0890 


0.1659 


14 


0.2244 


0.1122 


0.0714 


0.1429 


0.0826 


0.1541 


15 


. 2094 


0.1047 


0.0666 


0.1333 


0.0771 


0.1438 


16 


0.1963 


0.0982 


0.0625 


0.1250 


0.0723 


0.1348 


17 


0.1848 


. 0924 


0.0588 


0.1176 


0.0681 


0.1269 


18 


0.1745 


0.0873 


0.0555 


0.1111 


0.0643 


0.1198 


19 


0.1653 


0.0827 


0.0526 


0.1053 


. 0609 


0.1135 


20 


0.1571 


0.0785 


. 0500 


0.1000 


0.0579 


0.1079 


22 


0.1428 


0.0714 


0.0455 


. 0909 


0.0526 


0.0980 


24 


0.1309 


0.0654 


0.0417 


0.0833 


0.0482 


0.0898 


26 


0.1208 


. 0604 


0.0385 


0.0769 


0.0445 


. 0829 


28 


0.1122 


0.0561 


0.0357 


0.0714 


0.0413 


0.0770 


30 


0.1047 


0.0524 


. 0333 


0.0666 


0.0386 


0.0719 



GEARING 21 

diameter, that is, the diameter to which a blank must be turned 
before the teeth are cut, 2 must be added to the number of teeth 
in the gear and the sum divided by the diametral pitch. 

Thus outside diameter = — p — (7) 

Example. — What is the outside diameter of a gear having 40 
teeth and 4" pitch diameter? 

P = 

P = ^ or 10 



Outside diameter (0. D.) = 



N 


D 


40 
4 ^^ 


N + 2 


P 


40 + 2 



= 4.2' 



10 

16. Dedendum Circle. — The dedendum circle is the circle 

limiting the working depth of the teeth. Its radius is greater 
than that of the root circle by an amount equal to the clearance. 
It indicates the depth to which the teeth of the other gear fit 
into the spaces. Therefore, for standard teeth, the dedendum 
circle is the same distance inside the pitch circle that the adden- 
dum circle is outside the pitch circle. Consequently, the diam- 

. N - 2 
eter of the dedendum circle for standard teeth is — p — . 

17. Root or Clearance Circle. — A certain amount of clearance 
is usually cut at the bottom of the spaces between teeth to allow 
dirt and other foreign matter to work out of the gears without 
breaking the teeth. The amount of this clearance below the 
dedendum or working depth circle is left to the judgment of the 
designer, but it is customary to make it one-tenth of the thickness 
of the tooth. If P is the diametral pitch, the thickness of the 

1.57 
tooth will be half the corresponding circular pitch, or — ^• 

.157 
Hence, the clearance will be ^-p- • Since the depth of the stand- 
ard tooth is equal to the sum of the addendum, the dedendum, and 
the clearance, and since the addendum and dedendum are each 

1 • 1 1 

equal to pf the total depth to which the teeth are cut is p + p + 

0.157 2.157 
— 7T— or -^F, — 



22 



ADVANCED SHOP DRAWING 



18. Tables of Tooth Parts.— In Table 1 the items in the differ- 
ent columns are as follows: 

Column 1. Diametral pitch. 

Column 2. Circular pitch. 

Column 3. Thickness of tooth on pitch line. It will be noticed 
that the figures in this column are one-half of the corresponding 
figures in Column 2. This means that the thickness of the 
tooth is usually one-half of the circular pitch. 

Column 4. Addendum, or face of tooth. See Fig. 13. 

Table 2. — Gear Wheels 
Table of Tooth jParts — Circular Pitch in First Column 



Circular 
pitch 

P' 



Threads 

of teeth 

per inch 

linear 

1" 



Diametral 
pitch 



Thickness 

of tooth 

on pitch 

line 

t 



Addendum 
or 1" 

P 



Working 

depth of 

tooth 

D" 



Depth 
of space 

below 
pitch line 

s +/ 



Whole 
depth of 

tooth 
D" +f 



2 


H 


IH 


Hs 


IH 


f^i 


IH 


Hs 


IM 


y^ 


iKe 


^y2z 


IH 


Hx 


IH 


y^. 


iHs 


i^^i 


IH 


yf> 


iHe 


1^9 


iVs 


% 


iKe 


^yii 


1 


1 


1^6 


iKs 


Va 


IM 


^Ke 


l^fs 


H 


l>i 


H 


Wz 


iMe 


\yix 


H 


IM 


H 


1% 


H 


IH 


^ 


m 


Ke 


iH 


H 


2 


^ 


2>i 


Ke 


2H 


M 


2H 


H 


2M 


H 


2H 


Hi 


2H 


H 


3 


H6 


3K 


Ho 


3H 


H 


3M 



1.57D8 
1.6753 
1.7952 
1.9333 
2.0944 
2.1855 
2.2848 
2.3562 
2.3936 
2.5133 
[2.6456 
,2.7925 
2.9568 
3.1416 
3.3510 
[3.5904 
.8666 
.9270 
1888 
,5696 
4.7124 
5.0265 
5.2360 
5.4978 
5.5851 
6.2632 
7.0685 
7.1808 
7.3304 
7.8540 
8.3776 
8 . 6394 
9.4248 
10.0531 
10.4719 
10.9955 



1.0000 
0.9375 
0.8740 
0.8150 
. 7500 
0.7187 
0.6875 
0.6666 
0.6562 
0.6250 
0.5937 
0.5625 
0.5312 
. 5000 
0.4687 
0.4375 
0.4062 
0.4000 
0.3750 
0.3437 
0.3333 
0.3125 
0.3000 
0.2857 
0.2812 
0.2500 
0.2222 
0.2187 
0.2143 
0.2000 
0.1875 
0.1818 
0.1666 
0.1562 
0.1500 
. 1429 



0.6366 
0.5968 
0.5570 
0.5173 
0.4775 
0.4576 
0.4377 
0.4244 
0.4178 
0.3979 
0.3780 
0.3581 
0.3382 
0.3183 
0.2984 
0.2785 
0.2586 
0.2546 
0.2387 
0.2189 
0.2122 
0.1989 
0.1910 
0.1819 
. 1790 
0.1592 
0.1415 
0.1393 
0.1364 
0.1273 
0.1194 
0.1158 
0.1061 
0.0995 
0.0955 
0.0909 



1.2782 
1.1937 
1.1141 
1.0345 
0.9549 
0.9151 
0.8754 
. 8488 
0.8356 
0.7958 
0.7560 
0.7162 
0.6764 
0.6366 
0.5968 
0.5570 
0.5173 
0.5092 
0.4775 
0.4377 
0.4244 
0.3979 
0.3820 
0.3638 
0.3581 
0.3183 
0.2830 
0.2785 
0.2728 
0.2546 
0.2387 
0.2316 
0.2122 
. 1989 
0.1910 
0.1819 



0.7366 
. 6906 
0.6445 
0.5985 
0.5525 
. 5294 
0.5064 
0.4910 
0.4834 
0.4604 
0.4374 
0.4143 
0.3913 
0.3683 
0.3453 
0.3223 
0.2993 
0.2946 
0.2762 
0.2532 
0.2455 
0.2301 
0.2210 
0.2105 
0.2071 
0.1842 
0.1637 
0.1611 
. 1578 
. 1473 
0.1381 
0.1340 
0.1228 
0.1151 
0.1105 
0.1052 



1.3732 
1.2874 
1.2016 
1.1158 
1.0299 
0.9870 
0.9441 
0.9154 
0.9012 
0.8583 
0.8156 
0.7724 
0.7295 
. 6866 
0.6437 
. 6007 
0.5579 
0.5492 
0.5150 
0.4720 
0.4577 
0.4291 
0.4120 
0.3923 
0.3862 
0.3433 
0.3052 
0.3093 
0.2943 
0.2743 
0.2575 
0.2496 
0.2239 
0.2146 
0.2060 
0.1962 



GEARING 23 

Column 5. Working depth of tooth = Addendum + Deden- 
dum. Since the Addendum equals the Dedendum, the figures 
in this column are twice those of Column 4. 

Column 6. Depth of space below pitch line, ov flank of tooth. 
The figures in this column are greater than those in Column 5 by 
the amount of '^f,^^ which is the clearance; that is, the point of 
the mating tooth does not go below the working depth circle 
(or Dedendum Circle) as shown in Fig. 13. 

Column 7. Whole depth of tooth. 

Table 2 is similar to Table 1 except that the circular pitches 
instead of the diametral pitches are given in the first column. 

19. Velocity Ratio. — By velocity ratio is meant the number of 
revolutions, or the part of a revolution, that the driven gear 
makes for each revolution of the driving gear. Two gears in 
mesh are usually denoted as ''driver" and "driven," their desig- 
nation being self -apparent. Since the pitch circles are tangent 
in two gears that are in mesh, their velocity ratio may be cal- 
culated as if they were two rolls rolling together without slipping 
as in Fig. 14. If A and B were the same size and A the driver, 
then for each revolution of .4, B would also make one revolution. 
If B were twice the diameter oi A, it would take two revolutions 
of A to cause B to revolve once. This relation may be expressed 
in the form of an equation as follows : 

Revolutions of B Pitch diameter of A 



Revolutions of A Pitch diameter of B 



or 



■D ] f i R — (P^^ch diameter oi A) X (Revolutions of A) 

Pitch diameter of B 

Example. — ^If gear A with a pitch diameter of 4^' makes 
10 r.p.m., how many will gear B, with a pitch diameter of 8'', 
make? 

Let pitch diameter oi A = 4" 

Let pitch diameter oi B = 8'' 

Let revolutions per minute (r.p.m.) of A = 10 

To find r.p.m. of B 

4 X 10 . , ^ 

— Q = 5 r.p.m. for B 

o 

If the number of teeth in each of the gears is given, instead of 
the pitch diameters, the r.p.m. of B may be found in the same 
way. 



24 



ADVANCED SHOP DRAWING 



Example. — Thus, if A has 48 teeth and makes 30 r.p.m., what 
will be the r.p.m. of B having 20 teeth? 
48 X 30 



20 



= 72 r.p.m. for B 



If the revolutions of each of the gears and the number of teeth 
in one of them are known, the number of teeth in the other may 
be found as follows : 

rrt xu • D (Teeth in A) X (Revolutions of A) 

ieetn m n = ^^ , — —. ^r^^^ 

Revolutions of B 

Example.- — If A with 48 teeth makes 30 r.p.m., how many 
teeth has B if it makes 72 r.p.m? 

48 X 30 



72 



= 20 teeth for B 



If the number of revolutions of each gear and the pitch diam- 
eter of one are given, the distance between centers may be found 
by first determining the pitch diameter of the other gear and 
taking one-half the sum of the two pitch diameters. 




Fig. 16. — Annular or Internal gearing. 

Example. — If A with a pitch diameter of 8" makes 25 r.p.m. 
and B makes 100 r.p.m., what is the distance between centers? 

Let revolutions of il =25 
Let revolutions of 5 = 100 
Let pitch diameter of A = 8'' 



The pitch diameter of B will be 

8 X 25 
100 



= 2' 



GEARING 



25 



The distance between centers will be 

H(8 + 2) = 5" 

In the case of spur gears, the distance between the centers 
of the gears is the sum of their radii, but in the case of annular 
or internal gears, Fig. 16, the distance between centers is the 
difference of their radii. 

The simplest form of the general equation regarding the veloc- 
ity ratios of gears is: 

(Pitch diameter of ^) X (Revolutions of ^) = 

(Pitch diameter of B) X (Revolutions of B) 
In this equation, the number of teeth may be used instead of the 
pitch diameters. 

20. Special Gears. — Rack and Pinion. — If the diameter of 
one of the gears of Fig. 12 is imagined to be increased until it 
becomes infinite, it will then become a straight bar with teeth 
cut in its side meshing with a gear as in Fig. 17. Such a combi- 





FiG. 17. — Rack and pinion. 



nation is called a rack and pinion. The number of revolutions 
that the gear can make in one direction depends upon the length 
of the rack. 

Annular Gears. — An annular or internal gear is one in which the 
teeth are cut internally on the pitch circle, the rim being outside 
of the pitch circle. Figure 16 shoWs an annular gear and pinion 
in mesh. 

21. Gear Drawings. — Working Drawing of a Spur Gear. — In 
making a working dra>wing of a spur gear, complete data are 
usually not given. The draftsman must supply much that 
is necessary to make a complete shop drawing. In order to do 



26 



ADVANCED SHOP DRAWING 



this, it is necessary to know what the proportions of the various 
parts should be, to understand what the different dimensions are 
for and what is meant by the terms used. It is not necessary to 
show all the tooth outlines, although a few conventional teeth 
are generally drawn. 

Example. — Make a shop drawing of a 28 tooth, 4 diametral 
pitch spur gear; face 2'^; diameter of shaft l/iie"; length of hub 
2M'' projection on one side; 4 arms or spokes. 

Pitch Diameter. — The pitch diameter is 2% or 7". On a 
drawing, the pitch diameter of a gear should always be noted 



^ 2" J 




^^ 



28 T., 4. P., Spc»r Gear. 
|- Wanted Cast Iron. 

Fig. 18. — Working drawing of spur gear, 

either ''Pitch Dia." or ''P. D." as it is the most important di- 
mension. The conventional line for the pitch circle is a dash and 
two dot line as shown in Fig. 18. 

Outside Diameter. — From Table 1, the addendum of a 4 pitch 

1" 
gear tooth is p-= li" or .25''. The pitch diameter plus twice 

the addendum [7'' + (2 X .25'')] gives 7^" as the outside 
diameter. This may be drawn as in Fig. 18. 

Root Diameter.- — The root diameter is found by subtracting 
twice the sum of the addendum and the clearance; [2 (s +/)] 
from the pitch diameter: 7" - 2(.2893") = 6.421" +• This 
root diameter should be shown, although it is the practice in some 
shops to show rather the whole depth of tooth. If the gear were 



GEARING 27 

to be cast, it would then be necessary for the drawing to show the 
root diameter so the pattern maker would know what diameter 
to turn the blank upon which to fasten the teeth. 

Thickness of Rim.- — If the thickness of the rim is made }'2 of the 
circular pitch, it will be strong enough. From Table 1 the circu- 
lar pitch corresponding to 4 diametral pitch is .7854''. 

^^ — ^r— = .3927, thickness of rim 

Then 

Inside diameter of rim = (pitch diameter) — 2[(s + /) + rim 
thickness] 

Inside diameter of rim =7-2 (.2893 + .3927) 

Inside diameter of rim = 7 — 1.364 

Inside diameter of rim = 5.636'', say 5%" 

Choosing an approximate final dimension like this, it is better 
to choose the dimension that gives the greatest strength. 
. Diameter of Hub. — If the diameter of the hub is made 2 times 
the diameter of the shaft, it will be thick enough. 

Wi^" X2 = 2%", diameter of hub 

Length of Huh. — In this case the length of hub is given as 23-^". 
If it were not given, however, it should be at least equal in length 
to the diameter of the shaft, and is usually made greater. 

The specifications state that the hub shall project on one side, 
evidently to give clearance between the rim and a surface through 
which the gear shaft may project. Consequently, Fig. 18 shows 
the hub projecting 3^^" on one end, which is sufficient ' r a gear 
this size. 

Width of Arms. — The arms should be drawn of such ?ldth at 
the hub, that, if extended, they would be tangent to the shaft. 
At the outer end or near the rim they should be approximately 
J^o of the width at the hub. In this case the width of arm would 
be 13^^" at the hub and %" at the rim. These figures are for 
heavy transmission and can be reduced somewhat for light work. 
The arms are often made with a taper of 3^^" per foot. The sec- 
tion of the arms must be indicated. This can best be done by 
making a small revolved section on the arm as was done in Fig. 
18. 

Thickness of Arms. — If the thickness of the arm at each end is 
made equal to .4 of the width at each end, it will be strong enough. 
This gives approximately 3^^" and %", respectively. Where 



28 



ADVANCED SHOP DRAWING 



the gear is small, it is often made with a sohd web instead of p utting 
hjarms. 

Width of Face. — In this case the width of the face is given as 
2''. It should always be equal to at least 2 or 3 times the circular 
pitch. This is determined by the designer according to the load 
that the gear teeth must carry. 

Tooth Outlines. — The lines and dimensions shown in Fig. 18 
are all th.it are necessary for the gear to be made in the shop. 
Sometimes, however, a few teeth are shown in approximate out- 
line. If this is desired, they can be drawn as follows: 

Draw a radius of the pitch circle as in Fig. 19. On this radius 
draw a semi-circle with center at A . Bisect AB Sit C. With B 




Fig. 19. — Layout of tooth outline. 



as a ceiP^r and a radius BC, draw an arc intersecting the semi- 
circle ODB at D. With as a center and a radius OD, draw an 
arc EDF. Space out a few teeth on the pitch circle, as a, b, c, etc. 
With a radius DB and centers on arc EDF, draw arcs through the 
points a, h, c, etc. on the pitch circle, from the arc EDF out to the 
addendum circle. The part of the tooth between the arc EDF 
and the dedendum circle is drawn radial. To do this draw a 
straight line toward the center of the gear from the point where 
the tooth arc intersects the arc EDF. A small fillet, or arc, rounds 
the tooth outline from the dedendum circle into the root circle. 
Keys and Keyways. — The sizes of keys for use on shafts of vari- 
ous diameters are shown in Table 3. The width of the keyway 
in the shaft and in the hub is the same. Half the thickness of 



GEARING 



29 



the key way is cut in the shaft and half in the hub. In the case 
of armed wheels, the keyway should always be put in line with 
one of the arms. In this position, the keyway will weaken the 




Fig. 20. — Method of dimensioning keyways. 

hub less than if it were placed between two arms. Special short 
hubs sometimes have more than one key. Figure 20 shows 
a new method of dimensioning keyways in shafts and hubs. 



DIMENSIONING OF 


DIMENSIONING OF 


KEYWAY IN SHAFT 


KEYWAY IN HUB 


DIMENSIONS OF KEYS. 


DIAMETER 0F5HAFT5 


WIDTH 


THICKNESS 


INCHES 


INCHES 


INCHES 


1 -° 're 


3 
16 


3 

16 


\ -k TO 1 — 


5 


J. 


'8 16 


16 


4- 


',-6 ^0 ''i 


3 

a 


5 
16 


1 — TO 2 ^ 
' 16 "-' '^ 16 


1 

2 


3 
8 


2il TO 2\i 


1 


i 


2ll TO 3| 


1 


16 


^Te TO 3;i 


i 


1 


3|i TO 4| 




II 
16 


^S TO A^e 


, j- 

'8 


3 
4- 


4j TO 5 1 


1 


15 

16 


5i TO 6| 


1 
' 2 


1 


6^ TO 7| 


.3 
'4- 


'§ 



Table 3. 



This method has come into practice in late years and is desirable 
because it permits the mechanic to make a better fit between the 
key and keyway than is possible under the old method shown in 
Fig. 18. 



30 ADVANCED SHOP DRAWING 

Problem 7 

(a) In a gear having 48 teeth and 1" circular pitch, what is the pitch 
diameter? 

(6) A gear with 4" pitch diameter has 80 teeth; what is the pitch? 

(c) Two gears are in mesh. The driver makes 20 revolutions and the 
driven makes 15. The driver has 72 teeth and its diametral pitch is 8. 
How many teeth in the driven, and what is the distance between the centers? 

(d) In an annular gear and pinion, the pinion makes 3 revolutions while 
the annular gear makes 1 revolution. The pitch diameter of the pinion is 
4". What is the distance between the centers of the two gears? 

(e) In two spur gears that are in mesh, the distance between their centers 
is 15". If the driver makes 50 revolutions, while the driven makes 30, 
what are their pitch diameters, and how many teeth in each, if their diamet- 
ral pitch is 8? 

Problem 8 

Make a full size drawing of a spur gear of 36 teeth, 6 pitch; shaft diam- 
eter 1"; width of face l}i"; length of hub 2" with projection on one side; 
4 arms. Draw the same views as shown n Fig. 18. 



CHAPTER III 
GEARING (Bevel, Worm and Special Gears) 

22. Bevel Gears. — Bevel gears are gears used to connect shafts 
that intersect. Shafts meeting at any angle may be connected 
by bevel gears, though the great majority of bevel gears are found 
on shafts meeting at 90°. Figure 21 shows a pair of bevel gears, 
the axes of which intersect at an angle of 90°. ''Miter gears" is 
a special name sometimes given to two bevel gears of the same size 
connecting shafts at 90°. 

In the case of the spur gear, it was imagined that the teeth were 
developed on a rolhng cyhnder. In the bevel gear, the teeth are 





Fig. 21. — Bevel gearing. 

developed on a cone called the pitch cone, so that all dimensions 
of the teeth diminish toward the apex of the cone as can be seen 
in Fig. 21. 

Bevel gears are generally laid out in pairs, since one bevel gear 
will mesh properly only with its mate, and not with any other 
gear even of the same pitch. 

All calculations for bevel gears are made in exactly the same 
way as for spur gears. The pitch diameter of a bevel gear is the 
diameter of the base of its pitch cone. 

23. Bevel Gear Layout. — A drawing for bevel gears is not 
quite so simple as that for spur gears. A complete drawing of 
the gears, as 'shown in Fig. 21, is not necessary, however; a sec- 
tion through the axes generally being sufficient. Figure 22 shows 

31 



32 



ADVANCED SHOP DRAWING 



a drawing of a set of bevel gears with the angles and dimensions 
which are necessary for the shopman. 

Figure 23 is an enlarged partial view of the 32 tooth gear of 
Fig. 22. 

Example. — Make a drawing of a pair of bevel gears having 56 
and 32 teeth respectively, 8 pitch, shaft angle 90°. 

Pitch Diameter. — Referring to Fig. 22, pitch diameter of 
large gear = ^% or 7''. The axis of this gear is OB. 




Fig. 22. — Shop drawing of bevel gears. 



Pitch diameter of small gear = 32^or4". The axis of this gear is 
OA . Since the gears are to connect shafts at right angles, the lines 
OA and OB should be laid out for Y = 90°. On the hne OA lay 
out Oa = 3J^", the pitch radius of the large gear; on the line OB 
lay out Oh = 2", the pitch radius of the small gear. Through 



GEARING 33 

a and perpendicular to Oa draw MD. Through h and perpen- 
dicular to Oh draw CD. The point D where these lines intersect 
will be the ''pitch point/' the point where the pitch circles are 
tangent. Make Ma = Da and Cb = Db. From M, D, and C 
draw light lines to 0, dash and two dot lines as was done in Fig. 
18. These lines then form the sides of cones, the bases of which 
are MD and DC. These cones are called the ''pitch cones" 
and in bevel gears correspond to the pitch cylinders of spur 
gears. The angles X and X' formed by the sides of the pitch 
cones are called the "pitch angles." Through M draw MA 
perpendicular to OM; through D draw AB perpendicular to 
OD) and through C draw CB perpendicular to CO. The pro- 
jections of these three lines beyond the rims of the gears may later 
be erased from the finished drawing. 

Addendum. — On the three perpendiculars just drawn, MA, 
yl5, and5C, lay out from the three points M, D, and C the ad- 
dendum as taken from Table 1. For 8 pitch the addendum is 
.1250''. The new points just located represent the tops of the 
teeth at the outer surfaces of the gears. 

Depth of Teeth.— For 8 pitch the depth of tooth is 0.2696'', or 
the depth of space below pitch Hne is 0.2696 - 0.1250 = 0.1446". 
Laying off this distance in the other direction from C, D, and 
M gives the bottoms of the teeth at the outer extremities of 
the gears. 

Thickness of Rim. — The thickness of rim K is made approxi- 
mately equal to one-half the circular pitch, as in the case of 
spur gears. 

Backing. — The dimensions / and /' of the hubs are called the 
"backing" and are important dimensions. On account of the 
inclination of the teeth of a bevel gear, there is a pressure tend- 
ing to force the gears apart. Bevel gears must, therefore, be 
rigid and have hberal backing on the hubs. Each gear should 
have a shaft bearing and a thrust bearing as close as possible. 

If the drawing is laid out accurately, the outside diameters 
can sometimes be scaled with sufficient accuracy, the dimensions 
being given to the nearest hundredth inch. When this method is 
not considered accurate enough, the dimensions can be calcu- 
lated to thousandths or ten-thousandths of an inch. Some of 
the calculations given below are worked out very closely. It is 
necessary for the draftsman to have some knowledge of trigo- 
nometry in order to make these calculations. 



34 



ADVANCED SHOP DRAWING 



Pitch Angle. — By referring to Fig. 23, X', the pitch angle, can 
be found as follows : 

Oa = Zy^' = 3.5'' 
Ma = 2" (Angle MaO is a right angle) 

Mn 9 

Tan Z' = ^ = Tf^ or 0.5714" 
Oa 3.5 

X' = 29° 45' 




Fig. 23. — Enlarged view of bevel gear tooth. 

Outside Diameter. — ^The triangles MOa and eMd, Fig. 23, are 
similar, since their sides are perpendicular and each contains a 
right angle. 

Therefore, angle X' = angle eMd or 29° 45'. The side Md 
= 0.1250" for an 8 pitch gear as taken from Table 1. 

eM 



Cos eMd = 



dM 



Therefore, eM = dM cos eMd. 
By substitution 

0.1250 X 0.8682 = 0.10852". 

The Outside Diameter (O.D.) = Pitch Diameter (P.D.) + 2 
eM. 

Therefore, the O.D. = 4" + 0.217" = 4.217". 

Face Angles. — Drawing lines from the tops of the teeth to the 
center gives the angles W and W , Fig. 22, which are called 
the '^face angles." These lines represent the tops of the teeth 
and are the lines to which the gear blanks must be turned. 

To get the face angle, TF', the angle R of Fig. 23 must be added 
to the angle X'. First the length of the side OM must be found. 

Oa 



Cos X' = 



OM 



GEARING 



35 



Therefore, 

Tan/e = 
By substitution 



OM = -^% or .r4L = 4.031'' 



cosX' 
Md 
OM 
0.125 



0.8682 



= 0.03101 



4.031 
R = 1° 47', nearly. 
The face angle W = X' + R 

(29° 450 + (1°470 - 31° 32' 
Cutting Angles.- — The angles U and U\ Fig. 22, formed at 
by drawing lines from the bottoms of the teeth to are called 
the '^ cutting angles." 

The cutting angle, U', Fig. 23, is less than the pitch angle, X', 
by the amount of the angle S. 

Mc 



Tan *S = 



OM 



Therefore, 



Mc = 0.1446 " (From Table 1) 

^ 0.1446 ^^o-o^ 
tan S = ^^TTT^ = 0.03o87 



4.031 

>S = 2° 3', nearly 
The cutting angle U' = X' - S = (29° 45') - (2° 3') = 27° 42'. 




Fig. 2i. — Section view of bevel gear. 

Edge Angles. — The angles Z and Z', Fig. 22, at the backs or 
outer edges of the gears are called the "edge angles." 

The edge angle Z' = the pitch angle X'. 

The equations used above can be used only when the gear 
shafts make an angle of 90°, though the procedure for other shaft 
angles is similar. Most of the other dimensions are similar to 
those of spur gears. 



36 



ADVANCED SHOP DRAWING 



Figure 24 shows a bevel gear with the names of the various 
angles and parts. These are the dimensions and angles which 
should appear upon a shop drawing of a single bevel gear. The 
legend for a bevel gear should be similar to that shown in 
Fig. 18. 

The bevel gear shown in Fig. 24 has a plain web supporting 
the rim. If the gear is for heavy service, this web may be rein- 
forced by ribs from the rim to the backing. 

24. Worm and Worm Wheel. — The combination shown in Fig. 
25 known as the worm and worm wheel is used for connecting 
axes that are at right angles but which do not intersect. It is 
used for obtaining a large reduction in speed. 






Fig. 25. — Worm and worm wheel. 



Velocity Ratio of Worm Gears. — ^The velocity ratio does not 
depend upon the ratio of the pitch diameters, as in the case of 
gears connecting parallel or intersecting shafts, but rather upon 
the number of teeth in the wheel and upon whether the worm has 
a single or a multiple thread. 

The worm is the same as a screw thread and is shown in section 
in Fig. 26. If the worm wheel has 48 teeth, and the worm is 
single threaded, as in Fig. 27, it will take 48 revolutions of the 
worm to make one complete revolution of the wheel. If the worm 
is double threaded, as in Fig. 28, it will require 24 revolutions 
of the worm to turn the wheel once. Likewise, if the worm is 
triple threaded, 16 revolutions will be required for one turn of 



GEARING 



37 




SECTION ON LINE 
WORM AND WORM WHEEL. 

28t bronze wheel. 

^'■r,r.h. single thread steel worm 

'^"^% 
SECTION ON LINE A-B. 

Fig. 26. — Working drawing of worm and worm wheel. 




DEPTH OF THREAD 

->|PITCHk- 



FiG. 27. — Single threaded screw. 



38 



ADVANCED SHOP DRAWING 



the wheel, and so on. From this it will be seen that the pitch 
diameter of the worm does not affect the velocity ratio. 

Pitch. — The circular pitch is always used in a worm and wheel 
combination, since the worms are cut in a lathe. Lathes are 
not equipped with the proper change gears for cutting diametral 
pitches. 

I«-LEAD 




FiG. 28. — Double threaded screw. 

25. Shop Drawing of Worm and Worm Wheel. — As in the 
case of the bevel gears, it is not necessary to make a complete 
drawing showing the tooth outlines of the worm and wheel in 
order that they may be made in the shop. 

Figure 26 shows the necessary views and dimensions for a work- 
ing drawing. The left-hand view is a section through the axis 
of the worm wheel and an end view of the worm. The right-hand 
view is a section along the axis of the worm, although the wheel 
is shown in section only a't the rim. The sizes of the teeth are 
obtained from Table 2. The few teeth that are shown in the 
wheel may be drawn by the approximate method of Fig. 19. 
The angle Z, which the sides of the worm wheel make with each 
other, is usually made 60°, but it may be 90°. The 'Hhroat 
diameter" of the wheel is the same as the outside diameter of a 
spur gear of the same pitch and the same number of teeth. 

The face of the tooth is made concave to fit the worm. The 
teetxi on the wheel are cut by means of a ''hob." This is a cutter 
that looks a great deal like the worm except that its sides are 
fluted like a tap to form cutting edges. The diameter of the 
hob is greater than that of the worm by twice the clearance. 
It is necessary, of course, to use a different hob for every different 
diameter worm. 

If the drawing is made accurately, the outside diameter of the 
wheel can be scaled, and the dimension taken to the nearest 
hundredth of an inch: if greater accuracy is desired, it may be 



GEARING 



39 



calculated. This outside diameter is the diame.ter to which the 
blank, upon which the teeth are to be cut, must be turned. 

The thickness of the rim below the bottom of the teeth is 
made equal to one-half the circular pitch as in the case of spur 
and bevel gears. 

If the diameter of the wheel is not too great, it is made with a 
soHd web instead of spokes. This web is usually not over 3^^'' 
thick. 

26. Special Gears. — Stepped Gears. — In order to obtain 
smoother contact than is possible with a single pair of spur gears, 
several spur gears may be placed side by side on the same shaft 
and each turned so that its teeth are slightly in advance of the 




Fig. 29. — Pair of twisted gears. 

one of the preceding gear. Such a gear is called a ''stepped 
gear." If there are two gears thus stepped on a shaft, the com- 
bination is known as a gear of two steps. The gears are usually 
placed so that the teeth of one come opposite the spaces of the 
other, or one is stepped one-half the circular pitch ahead of the 
other. There are twice as many teeth in contact at one time in 
these gears as there would be in a single pair of spur gears. 

Twisted Gears. — The number of steps on a stepped gear may 
be increased indefinitely. If this be done it may be imagined 
that the face of each step be decreased so that the resulting gear 
has the same width of face as a spur gear. As a further illus- 



40 



ADVANCED SHOP DRAWING 



tration, a gear may be considered as made of some plastic material 
such as rubber. If one end be fixed and the other twisted about 
its axis, and the teeth thus twisted be given a set form, the 
resulting gear will be what is known as a ^'twisted gear." Such a 
pair of gears is shown in mesh in Fig. 29. In a pair of twisted 




Fig. 30. — Train of twisted gears. 

gears, one of the gears always has a right-handed thread, and 
the other has a left-handed one. In the gear train shown in 
Fig. 30 the two gears B and C are twisted gears. 

Pitch for Twisted Gears. — There are three kinds of pitches used 
for twisted gears — normal, circular, and axial. Normal pitch is 
the shortest pitch distance between two consecutive teeth. It is 




Fig. 31. — Showing pitches for twisted gears. 

the distance ah, Fig. 31, and is measured on a line normal to the 
tooth outline. The normal pitch determines the cutter to be used. 
Circular pitch is the pitch distance between two teeth, measured 
in a plane vertical to the axis of the gear, as in the case of spur 
gears. It is the distance ac in Fig. 31. 



GEARING 



41 



Axial pitch is the pitch distance between two teeth, measured 
on a hne parallel to the axis of the gear. It is the distance ad in 
Fig. 31. 

Tooth Angle. — ^The tooth angle is the angle made by the tooth 
with the axis of the gear. It is the angle e in Fig. 31. This 
angle is sometimes called the '^spiral angle" or ''helical angle." 

Velocity Ratio of Twisted Gears. — The velocity ratio of twisted 
gears depends upon the number of teeth and the pitch diameters 
of the gears. The velocity ratio rules of spur gears are directly 
applicable to twisted gears; in fact, twisted gearing may be 
considered as a special case of spur gearing. 

In order for two twisted gears to mesh properly, they must 
have the same pitch and the same tooth angle. 




Fig. 32. — Herringbone gears. 

Herringbone Gears. — When two twisted gears are in mesh, they 
exert a thrust upon each other due to the curvature of the teeth, 
and thus tend to force each other in opposite directions along 
their respective shafts. This thrust may be taken up by thrust 
bearings or by placing together two twisted gears with equal but 
opposite tooth angles. Such gears, shown in Fig. 32, are known 
as ''herringbone gears." 

Spiral Gears. — Spiral or helical gearing is another name applied 
to twisted gearing. The term "twisted gears," however, always 



42 ADVANCED SHOP DRAWING 

applies to twisted gears on parallel shafts. Both gears of the 
pair have opposite handed threads, or spirals. '' Spiral or helical 
gears" is a name applied more generally to twisted gears on shafts 
that are not parallel. In this case both gears of the pair always 
have the same handed thresLds or spiral, either right- or left-handed. 
The gears A and B, Fig. 30, form a pair of spiral gears. Worm 
gearing is the limiting case of spiral gearing; in fact, the transition 
of gears may be traced from the common spur gear to the twisted 
gear, to the spiral gear, and to the worm, successively. 

Pitches for Spiral Gears. — Spiral gears, like twisted gears, have 
the same three pitches — normal, circular, and axial. As for 
twisted gears, these pitches involve the tooth angle. The tooth 
angle in spiral gearing is highly important as it affects the velocity 
ratio. 

Velocity Ratio of Spiral Gears. — The velocity ratio of spiral 
gears does not depend upon the pitch diameters of the spirals. 
Instead, it depends upon the number of teeth, the revolutions being 
inversely proportional to the number of teeth as in the case of 
the worm and worm wheel. Since the number of teeth is depend- 
ent upon the tooth or helical angle, this angle becomes an im- 
portant factor in the determination of velocity ratios. 

On account of the curvature of the teeth of spiral gears, and 
the sliding motion with which they mesh, an end thrust is always 
produced on their shafts. When the gear shafts are at 90°, this 
end thrust is least. The efficiency of the gears is highest when 
the tooth angle of the gears is 45°. 

As in the case of twisted gears, the normal pitch determines 
the pitch or size of the cutter, either spur or special, that will be 
used in cutting the teeth. From this normal pitch and the tooth 
angle, the designer must compute the circular pitch, and finally 
the pitch diameter of the gear desired. The addendum is the 
same for spiral and spur gears. Consequently, if twice the adden- 
dum be added to the pitch diameter, the diameter of the blank 
from which the spiral is to be turned may be obtained. 

It may be assumed that Fig. 31 represents a blank for a spiral 
gear, and that the inclined lines represent the centers of gear 
teeth. Then the angle hac equals the tooth angle e, because their 
sides are perpendicular. 

Furthermore, 

ah ah 



ac = 



cos hac cos e 



GEARING 43 

Hence, it may be stated as a general proposition for spiral 
gears that 

, ., , normal pitch 

circular pitch = — rr r 

cos tooth angle 

If the circular pitch and number of teeth are known, the pitch 
diameter can be found readily. 

Example. — Two spiral gears with a velocity ratio of 1 to 1, 
and with the shafts at 90° are to be cut with a B. & S. (Brown 
& Sharpe) 16 pitch cutter. Find the size of blanks required for 
18 teeth. 

Since the shaft angle is 90°, the gears should have tooth angles 
of 45° for maximum efficiency. The teeth of the gears may be 
either both right-handed or both left-handed, depending upon the 
conditions of the problem. By reference to Table 1, it is found 
that for a 16 pitch cutter the normal circular pitch is 0.1963. 
Hence, 

^. , ., , normal pitch 

Circular pitch = ^ — ~ r 

cos tooth angle 

Substituting Circular pitch = — — ~^ 

cos t:0 

The pitch circumference = circular pitch X No. of teeth, or 
0.277 X 18 = 4.986'' 

pitch circumference 



The pitch diameter = 



4.986 



= 1.587" P. D. 



3.1416 

The diameter of blank = pitch diameter + 2 X addendum. 
For 16 pitch, the addendum is 0.0625 (Table 1) 

Hence, 

0. D. = P. D. + 2 X addendum 
or 

O. D. = 1.587 + (2 X 0.0625) 
= 1.587 + 0.125 
= 1.712'' 

When the velocity ratio of two spirals is other than 1 to 1, it can 
not be determined from the pitch diameters as in spur gearing 
as before stated. Instead, it must be determined from the tooth 
or helical angle of each gear. If the tooth angles of both gears 
are the same, the velocity ratios will be inversely proportional 



44 ADVANCED SHOP DRAWING 

to the pitch diameters. If the tooth angles are different, this 
rule will not apply since the axial pitch, and, therefore, the number 
of teeth, will vary. In the case of the single threaded worm, 
the velocity ratio of the worm to the worm wheel is simply as 
1 to the number of teeth in the wheel. Increasing or decreasing 
the pitch diameter of the worm affects the tooth angle of both 
worm and worm wheel, but does not affect the velocity ratio, 
as long as the number of teeth in the wheel remains the same. 

The velocity ratio in all cases depends upon the number of 
teeth and the tooth angle. Hence, the velocity ratio of two gears 
is proportional to their pitch diameters only when their tooth 
angles are the same. The sum of the tooth angles must always 
be equal to the angle between their shafts; and, if the end thrusts 
of both are to be equal, their tooth angles must also be equal. 
When the tooth angle of one gear is greater than that of the other, 
the one with the greater tooth angle should be used as the driver. 

Example. — Two spiral gears with axes at 90° and a velocity 
ratio of 2 to 3, are to be cut with a 16 pitch cutter. The pitch 
diameter of the driving gear is IM", and its tooth angle 60°. 
Calculate the other dimensions of the gears. 

It was learned from Article 14 that the product of the diam- 
etral pitch and the circular pitch is a constant and equals t, or 

P' = — 
P 

The normal circular pitch of the driver is 

P' = ^^^ or 0.19635'' 
lb 

In the case just considered, the circular pitch is 

0.19635 
cos 60° 
= 0.3927 

Number of teeth = ' or 12. 

Since the velocity ratio is 2 to 3, and the driver has 12 teeth, the 
number of teeth in the driven may be determined easily. 

If "x^' represents the number of teeth in the driven gear, then 

2 :3 = 12 :x 
Therefore, x = — - — or 18 teeth 



GEARING 



45 



The angle between shafts is 90°. Since the tooth angle of the 
driver is 60°, the tooth angle of the driven must, therefore, be 
90° - 60° = 30°. 

The normal circular pitch of the driven is 

P' = 0.19635 

P = — — ^„o or 0.2267, the circular pitch of the driven 
cos 30 

D = 0.2267 X 18 or 1.298, the pitch diameter of the driven 

The diameters of the required blanks upon which to cut the spirals 

2 

are obtained by adding p to the pitch diameter of each gear. 

For 16 pitch (P= 16) the addendum is 0.0625 or ^ = 0.125. The 
resulting blank or outside diameters are, therefore, 

1.5'' + 0.125'' = 1.625" for driven 
and 1.298" + 0.125" = 1.423" for driver 

The number of the cutters to be used for cutting the teeth of 
the spiral gears is next determined. The tooth outline is con- 
sidered to be on a plane perpendicular to the helical outline of 
the teeth. Figure 33 shows a spiral gear of pitch diameter D, with 




Fig. 33. — Spiral gear blank. 

the inclined lines representing the center lines of the spiral teeth. 
If a plane AB be passed normal to the tooth outline, its true 
section may be projected, on lines normal to itself, as an ellipse 
C E F G. If the teeth were shown in outline on this ellipse, 
the teeth at G would show the true tooth outline produced by the 
cutter. This is the point of greatest curvature on the ellipse. 
The circle of equal curvature will be the ''equivalent spur gear'' 



46 ADVANCED SHOP DRAWING 

having the proper number of teeth for which the cutter must be 
chosen. This circle, G H J K, is shown in outhne. It can be 
proved by involved mathematics that if 

N = No. of teeth in spiral gear 
A^' = No. of teeth in equivalent spur gear 
e = tooth angle 



then 



N 

N' = ^V (8) 

cos"^ e 



If this formula is applied to the problem under consideration, 
it will be found that 

12 

^' = — TTTFTS 01* 96, tooth cuttcr for driver 
cos^ 60 

and 

18 

^' = TTTT^ or 28, tooth cutter for driven 

cos^ 30 

These are the numbers of cutters to be used on the two spiral 
gears, respectively. Since the cosine of an angle is always less 
than unity, the cube of the cosine will be much less and, conse- 
quently, N' will always be greater than N. 

Problem 9 

Make a full size drawing of a pair of bevel gears of 48 and 36 teeth; 8 
pitch, shaft angle 90°; diameter of shafts iHe"') backing 1^" and IM" 
respectively, and width of face l^-^". Each gear is to have a single 
key way, the dimensions of which may be obtained from Table. 3. All 
necessary angles and dimensions are to be shown. 

Problem 10 

Make a full size drawing of a single thread worm and worm wheel com- 
bination. Teeth in wheel 36"; pitch ^^"; distance between centers 
4^^"; diameter of worm shaft iHeJ diameter of wheel shaft l^fe"; 
length of worm 3"; length of wheel hub 2}i". 

(Note: Use Table 2 for finding the size of teeth. Use a 12" X 18" 
sheet for the drawing.) 

Problem 11 

Make a complete detail mechanical drawing of some gear of any type 
which may be readily accessible. Be sure that the drawing gives all the 
information necessary to make the gear. 



CHAPTER IV 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 

27. Isometric Drawing. — The work discussed thus far is known 
as mechanical drawing or orthographic projection. The different 
views of the object were projected upon planes parallel to the 
faces of the object. 

In making sketches or drawings it is often desirable to show 
the entire object in one view. Sometimes such a drawing can be 
readily made and be easily understood by one who does not under- 
stand ordinary mechanical drawing. In photography, the opera- 
tor generally takes a view of an object from one corner so as to 
give as complete an idea as possible, by showing the length, 
breadth, and depth of the object. So in pictorial representation, 
three faces of the object are usually shown in one view; in other 
words, the draftsman works from three axes, along which the 
various lines of the drawing 
are laid out. There are 
various methods of pictorial 
representation in use but the 
most important are isornetric 
and cabinet. 

In an isometric drawing 
the three axes make angles 
of 120° with each other. 
These are known as the 
isometric axes. One of the 
axes is usually vertical and 
the other two make angles of 30° with the horizontal. It is not 
necessary, however, that one of the axes should be vertical as 
long as the three axes make angles of 120° with each other. 

A mechanical drawing of a block 2J^" square and 4" long, 
drawn half size, is shown in Fig. 34. Figure 35 is an isometric 
drawing of this same block. An isometric drawing of this block 
standing on end would appear as in Fig. 36, the only difference 
being that edge ad is laid off on the vertical axis. The lines 
ah, ac, and ad make angles of 120° with each other. 

47 











b 








« r ■• ^ 




a 




d 




J 


* -2 " 








b 


a 
c 




1 


a 

c 




d 



Fig. 34. — Mechanical drawing of block. 



48 



ADVANCED SHOP DRAWING 



One of the isometric axes is spoken of as being vertical. As 
a matter of fact only its projection is vertical. In Fig. 36 the ob- 
ject is swung about the point a, or, the eye is above the surface 
abd and looking down on the block. Hence, none of the axes 
are seen in their true lengths, nor are the lines which are laid out 
along them. All dimensions appear shorter, or ''fore-shortened," 
and should, if the drawing were made correctly, be drawn to a 
smaller scale. This is ordinarily not done, as it complicates the 
drawing. It is unnecessary for the reason that the dimensions 
are fore-shortened in the same proportion along all the axes. The 





Fig. 35. — Isometric drawing of block 
shown in Fig. 34. 



Fig. 36. — Isometric drawing of 
block standing on end. 



full dimensions of an object are usually laid down. The error 
merely results in making the object look larger than it is, although 
the various parts are relatively proportioned. 

It is well known that in actual pictures, parallel lines appear 
to meet in the distance, like the rails of a railroad track. For the 
sake of; ^simplicity, parallel lines are drawn as parallel lines in 
isometric drawing as in the case of the square block just con- 
sidered. Broken lines are usually omitted from an isometric 
drawing unless necessary to give a full ^jud clear conception of 
the object. 

Lines not parallel to any of the isometric axes are known as 
non-isometric lines. It must be remembered that measurements 
can be laid down only on isometric lines; that is, on lines parallel 
to the isometric axes. To lay down such non-isometric lines, an 
isometric construction must first be built up from known iso- 
metric lines. If it is desired to make an isometric drawing of a 
segment of a hexagonal bar, one may proceed by the steps 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 49 



shown in Fig. 37, first making a mechanical drawing of two 
views, and then, by drawing a circumscribing rectangle about 
the hexagon of the upper plan locating the corners in isometric. 





Fig. 37. — Mechanical and isometric drawings of segment of hexagonal bar. 

A circle in any isometric plane always appears as an ellipse. 
It may be drawn either by coordinate projection, as in the case 
of the hexagon, or it may be drawn by the following approximate 









t^ 


^ 




<h- 






b/-/^-. 


>ca-^d 


J 


< 

t 


1 






^ 

^ 


¥ 


sC< 


> 


' 


f 


. 




1 






\ 




^-^^" 


'J^ 








'^ 


\ 




^ 







Fig. 38. — Isometric drawing of segment of round bar. 

method. It may be assumed that it is desired to show a 4'' 
segment of a 2J^" round bar in isometric. First the circumscrib- 
ing 23-^'' square, Fig. 38, should be drawn. Since a circumscribing 

4 



50 ADVANCED SHOPJDRAWING 

square is tangent to its inscribed circle at the middle point of each 
side, it follows that the same holds true of its isometric projection; 
that is, the circle must be tangent to the square ahcd at the mid- 
points of its 4 sides, or at points, e, f, g, and h. Since the radius 
of a circle or arc is always perpendicular to the tangent at the 
point of tangency, lines perpendicular to the sides of the square 
at their mid-points should be drawn, these being the construction 
lines ga, ha, fc, and ec. Since the sides of the square make angles 
of 30° with the horizontal, these lines can be readily drawn per- 
pendicular to their respective sides by drawing them at angles of 
60° with the horizontal. On account of the similarity and 
equality of the triangles thus constructed, it is found that the 
centers for the upper and lower arcs are in the upper and lower 
corners of the square. The centers for the two end arcs are at 
the points where ce and cf intersect on the line hd. With c as 
center a!nd/c as radius, arc/e should be drawn; with a as center 
and radius ga, arc gh should be drawn; with k as center and radius 
gk arc gf should be drawn; with m as center and radius Am arc he 
should be drawn. It will be noticed that fc = ga and gk = hm. 

A line ^" below hd and parallel to it will be the corresponding 
line upon which to construct the base of the cylinder. The 
elliptical form of the bottom will be exactly like the elliptical form 
of the top. It may be drawn by projecting the centers k and m 
along the lines ko and mr, and drawing the same corresponding 
arcs from the points o and r as centers, then connecting these with 
an arc of radius equal to cf. This drawing shows all the construc- 
tion lines that are necessary. These lines may be erased from 
the finished drawing. 

Figure 39 includes a mechanical drawing and an isometric 
drawing of a 4'' X 3'' X %" angle iron with rivet holes. This 
isometric drawing illustrates the principles of isometric represen- 
tation and serves to show the adaptability of this method- for 
simple cases. It should be noticed that all the lines of this 
sketch are either vertical or make angles of 30° with the hori- 
zontal. The rivet holes, being circular, are laid out by first 
drawing circumscribing squares whose sides make angles of 30° 
with the horizontal. The method of constructing these rivet 
holes and the %" fillet is shown in the enlarged views. It 
should be noticed that the holes appear different in the 
horizontal and vertical parts of the angle iron, although the 
construction is the same. If the accurate curvature of the 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 51 

%" fillet or any other such arc is desired, it may be deter- 
mined by the construction shown in the small sketch. The 
two isometric lines may be considered as parts of a square. 
The arc will be tangent to the two isometric lines, and the two 
points of tangency will be mid-points on a %" isometric square 




ff^^^^^^l , 



3- 
5'- 





-* 

1 1""^ 


8 


<- 







u 


t 


— 




lOlQO 


1 ' 1 
1 1 




♦ 


-• 4"— 


^ 






DETAIL OF 
CONSTRUCTION 
OP i" FILLET 




Detail of Construction of 
Hole in Horizontal Part. 



Detail of Construction or 
Hole in Vertical Part. 



Fig. 39. — Mechanical and isometric drawings of 4" X 3" X %" angle iron. 



constructed on these two iosmetric lines. Therefore, ab and ac, 
each equal to %", are laid off. At c and h, perpendiculars to 
the two lines respectively are erected. From their point of 
intersection d, as a center, an arc of radius db is struck. This 
arc is the required fillet. 

In Fig. 40 a mechanical drawing and an isometric drawing of 



52 



ADVANCED SHOP DRAWING 




Fig. 40. — Isometric and mechanical drawings of bearing block. 




Fig. 41. — Detail drawing of bearing block. 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 53 

the bearing block of Fig. 41 are shown. This figure shows all the 
necessary construction lines, but these should not appear on the 
finished drawing. The absence of broken lines should be noticed. 
A l}y^" square head nut blank with all construction lines is 
represented in Fig. 42 in both mechanical and isometric drawing. 
It should be noticed how the chamfer is provided for. 




Fig. 42. — Drawings of 1 34" square nut blank. 

28. Cabinet Drawing. — Cabinet drawing is somewhat similar 
to isometric drawing but is simpler because of the fact that two 
of the axes are at right angles to each other. Upon these two 
axes all dimensions are laid out to full scale. The other axis 
may be at any angle whatever, the only difference in using the 
various angles being that the object will appear to be viewed from 



54 



ADVANCED SHOP DRAWING 



different angles. It is usual to draw the third axis on some 
common angle to the horizontal as 30°, 45°, or 60° as these angles 
can be laid down easily with the draftsman's triangles. In this 
book the oblique angle of 45° will be used. 

If dimensions are scaled full size on the oblique axis, the ob- 
ject appears to be distorted. A cabinet drawing of a cube is 




ZZT^ 



Fig. 43. — Incorrect method of 
cabinet drawing. Oblique dimen- 
sions full size. 



Fig. 44. — Correct method of 
cabinet drawing. Oblique dimen- 
sions half size. 



shown in Fig. 43 where the oblique dimensions are scaled full 
size. The great distortion should be noticed. To overcome this, 
dimensions on the oblique axis should be drawn half size. Figure 
44 shows a drawing of the same cube with the oblique dimensions 
drawn to half size. The horizontal and vertical dimensions of 
these figures are full size as is the case in all cabinet drawings. 





Fig. 45.— Cabinet drawing of block. Fig. 46. — Cabinet drawing of round bar. 

A cabinet drawing of the square block which was shown in iso- 
metric in Fig. 35 is shown in Fig. 45. Figure 46 represents a 
cabinet drawing of the round bar which was shown in isometric in 
Fig. 38. It should be noticed that the end view of each is shown 
as a full end view regardless of the fact that the objects are 
viewed obhquely. The end view of Fig. 46 is a circle. 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 55 

An orthographic projection of the front of a tool chest is shown 
in Fig. 47, while a cabinet drawing of the same tool chest is shown 
in Fig. 48. The front of the chest in this figure is exactly the 
same as in Fig. 47. Figure 49 shows a cabinet drawing of the 
same chest with the drawers pulled part way out. ; 



o 




o 


6 




6 


o 




o 


6 


II 






Fig. 47. — Front view of tool chest. 



^ 



o II o 




Fig. 48. — Cabinet drawing of tool chest. 




Fig. 49. — Cabinet drawing of tool chest with drawers out. 



In Fig. 50 is shown the cube of Fig. 44 with circles inscribed 
on its faces, together with all the necessary construction lines. 
The front face is, of course, drawn full size, and the circle appears 
in full size inscribed in the square. This can be drawn most 
readily by drawing the two diagonals of the square and then, 
from their intersection as a center, striking a circle tangent 



56 



ADVANCED SHOP DRAWING 



to the sides of the square. The obhque hnes are drawn at an 
angle of 45°, and dimensions laid off to half scale along them. 

The projection of the upper surface hcde, being four-sided and 
having opposite sides parallel, is shown as a parallelogram. 
The projection of the circle will lie within this parallelogram and 
will be tangent to its four sides. It may be drawn as follows: 

The middle points of the four sides as /, g, h, and k are located. 
Then dh, gh, and fk are drawn. Next shis bisected at n and fm 
at 0. With radius nh and center n an arc is drawn tangent to 
line de. With radius bh and a center located by trial, another 




Fig. 50. — Cabinet drawing of cube with inscribed circles. 

arc is drawn that will connect the upper end of the arc just 
drawn and will be tangent to line cd. With the same radius 
hh another arc should be struck that will connect the lower end of 
this arc and will be tangent to the line be. The same procedure 
should be followed with o as a center and of as a radius and also 
with the arc tangent to be at k. 

The construction of the circle on the side face of the cube is 
similar. Any circle in cabinet projection can be thus readily 
drawn by first constructing the parallelogram which encloses it. 

Figure 51 shows a cabinet drawing of the bearing block which is 
shown by orthographic projection in Fig. 41 and by isometric 
drawing in Fig. 40. It should be noticed how the projection of 
the cylindrical part beyond both ends is provided for. The 
broken lines show how the contour of the ends would be shown if 
they did not project. Their centers would be at points a and c, 
respectively. Because of the projection of the ends, however, 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 57 

the centers of the ends must be offset by the distances ah and 
cd, respectively, equal to half of the projections at either distance. 
The bearing block, being irregular in outline on one face and 
of uniform outline throughout, is admirably adapted to cabinet 
drawing. In drawing such objects, the face with the irregular 
outline should always be placed in the plane of the paper; that 
is, the plane represented by the horizontal and vertical axes. 




Fig. 51. — Cabinet dra-wing of bearing block of Figs. 40 and 41. 



29. Shading Drawings. — The shading of drawings is sometimes 
resorted to in order to make them appear more realistic. Shaded 
drawings are commonly used in engineering catalogs, display 
drawings, illustrations, patent office drawings, and the like. In 
fact, they are commonly used where they will be placed in the 
hands of people who might not understand an unshaded mechan- 
ical drawing. Patent drawings must be shaded in such a manner 
that they will be readily understood by attorneys and others 
concerned with the granting of patents, who may have no 
knowledge of mechanical drawing. 

In shading drawings, the draftsmen should always assume that 
the light ^strikes the object from over the left shoulder. 

There are two methods of shading drawings: (1) by shade lines; 
(2) by line shading. The first method is the simpler. 

30. Shade Lines. — In all previous discussion, object lines were 
assumed to be made of- uniform weight. This is the general 
practice for all working drawings, and should be rigidly adhered 
to unless for some specific reason. 



58 



ADVANCED SHOP DRAWING 



In shading drawings, it is assumed that the light comes from 
over the left shoulder and strikes the object diagonally so that 
some of the surfaces are in the light while others lie in'the shadow. 
Edges of an object which lie between light and dark surfaces are 
often represented by lines two or three times as wide as the other 
lines as illustrated in Figs. 52 to 56. Such lines are called 
shade lines. 




Fig. 52. — Illustration of first rule of shade lines. 

In order to avoid the confusion that might arise as to just 
which lines should be shaded, the four following rules are ad- 
hered to in general practice and apply to the shading of all views 
of mechanical drawing. 

1. Shade right-hand and lower edges in all views. 

2. Shade left-hand and upper edges of all holes. 




Fig. 53. — Illustration of first and second rules of shade lines. 

3. Do not shade the lines representing the junctions of visible 
surfaces having equal illuminations. 

4. Shade the lower right-hand quadrants of outer circles and 
the upper left-hand quadrants of inner circles. 

The first rule is illustrated by Fig. 52 which is a shade line 
mechanical drawing of a cube, the front elevation and right side 
views being shown. 

The second rule is illustrated by Fig. 53 which shows a shade 
line drawing of a capping stone for a chimney. The lines to the 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 59 

right and bottom of the outhne are shaded according to the first 
rule, and the shading cf the two rectangular holes is in accordance 
with the second rule. 

The third rule must always be applied with a full consideration 
of the conditions involved. A mechanical drawing of a pyramid 
with the top cut off is illustrated in Fig. 54. The inclined lines 
in the left view are evidently governed by the third rule. A 





Fig. 54. — Illustration of third rule of shade lines. 

closer study will show that the inclined surfaces above and to 
the left are both illuminated and, therefore, the inclined line 
separating them is a light one. Since the inclined surfaces 
below and to the right are both shaded, a light inclined line will 
separate them. The other two inclined lines in this view separate 
illuminated and dark surfaces, and are, therefore, shaded. The 
lower inclined line in the right side view will be shaded if it 
makes an angle of 45° or less with the horizontal. 




Fig. 55. — Illustration of fourth rule of shade lines. 

The ring shown in Fig. 55 illustrates the popular method of 
shading inner and outer circles, according to the fourth rule. 
To shade a circle, it should first be drawn with a weight of line 
equal to the lightest part of the finished circle. The center of 
the circle should then be stepped upward to the left, on a line 
making 45° with the horizontal, a distance equal to the required 
width of the most heavily shaded part of the circle. With this 
new center and the same radius as before, a new semi-circular 



60 



ADVANCED SHOP DRAWING 



arc may be described tapering off gradually at its extremities 
into the circle originally drawn. 

Figure 56 is a shade line mechanical drawing of a slotted link 
and shows the application of the four essential rules of shade lines. 

When the above rules are applied to isometric drawing, 




Fig. 56. — Slotted link illustrating the four rules of shade lines. 

they are somewhat confusing. The popular practice among 
patent draftsmen and others using this method of illustration is 
to briilg out the nearest outside edges and the farthest inside edges 
with heavy lines as illustrated in the isometric drawing of the 
slotted bar, Fig. 57. 

In all work in shading drawings, the draftsman will find it 
necessary to use judgment and common sense. It should be 





Fig. 57. — Shade line isometric drawing 
of slotted bar. 



Fig. 58. — Line shading of pipe 
union. 



remembere/1 at all times that a shade line should lie between a 
light and a dark surface and that the light is coming from the 
upper left-hand corner of the paper. 

31. Line Shading. — ^The ability to do good line shading is an 
unusual accomplishment among draftsmen because it is so 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 61 



rarely used. It requires a great deal of practice and artistic 
ability on the part of the draftsman to use it rapidly and effect- 
ively. Often, the artistic shading of one view will obviate the 
necessity for any more views. 

The line shading of a simple object is illustrated in the shaded 
drawing of the union, Fig. 58. This figure also illustrates the 
two essential rules of line shading. 

1. A surface in the light grows darker as it recedes from the 
eye as shown by the shading on the left face of the hexagonal 
ring. 

2. A surface in the shadow grows lighter as it recedes from the 
eye as shown by the shading on the right face of the hexagonal 
ring. 

By this method the light is assumed 
to come over the left shoulder of the 
draftsman, making angles of 45° with 
the paper as it is held vertically in 
front of him. 

The Cylinder. — The top and front 
views of a vertical cylinder are shown 
in Fig. 59. The top view is shown to 
determine the shading of the front 
view. The arrows show the projec- 
tions of the light rays striking the 
cylinder diagonally at an angle of 45° 
with the paper. 

The Brilliant Line. — The brilliant 
line is the line where the object ap- 
pears to be most highly illuminated. 
In the top view, Fig. 59, the point a 
receives the most direct and strongest 
light, since the light rays as shown 
by the arrow are vertical to the 
circle at that point. The point c, 
however, midway between a and h, reflects the strongest light to 
the eye as shown by the downward arrow at the point. The 
unshaded area in the front view beneath the vertical arrow at c 
is known as the brilliant line. 

The darkest shadow in the front view appears beneath the 
point d where the light ray in the top view is tangent to the 
circle. 




Fig. 59.- — Line shading of 
cylinder. 



62 



ADVANCED SHOP DRAWING 



Having thus located the lightest and darkest parts of the 
cylinder, the two rules for line shading should be applied. The 
shading should increase in depth as it recedes on each of the 
brilliant lines. To the right, the shading increases in depth up 
to the line of darkest shadow. Beyond this point, the cylinder 
lies wholly within the shadow and the shading must, therefore, 
become lighter toward the right as it recedes from the eye. 

Flat and Graded Tints. — ^There are two kinds of line shades; 
namely, flat and graded tints. The flat tint has lines of uniform 
weight and equally spaced throughout as shown in Fig. 60 at yl . 
It is used on fiat surfaces in the plane of the paper, but only when 
the drawing is to be heavily shaded. Patches of it are sometimes 
used on such surfaces to indicate '^high lights." 

Graded tints show shading of increasing depth either to the 
left or to the right as shown in Fig. 60 B and C. Graded 




B C 

Fig. 60. — Flat and graded tints of line shading. 



tints were employed in the shading of the union. Fig. 58 and in 
the cylinder, Fig. 59. In graded tints, the setting of the pen is 
not changed for every line, but several lines are drawn with one 
setting of the pen. The pen is then reset and another 
series drawn. For flat surfaces the spacing of the lines should 
be uniform, but for curved surfaces the spacing between the 
lines should be decreased gradually toward the darkest part. 
Figure 60 shows the uses of all these shadings in the bolt. 

It is usually necessary to practice freely before attempting to 
apply shading to a finished drawing. As a first aid, the spacing 
of the lines and also their widths should be checked off by short 
dashes. When the gradation of these appears satisfactory, the 
line shades, similarly graded, may be added. All spacing and 
widths of lines should be gaged by the eye. 

32. Special Cases. — The Hollow Cylinder. — Figure 61 illustrates 
a section drawing of a hollow cylinder properly shaded in the 
front view by the aid of the auxiliary top view. The arrows 
indicate the projections of the light rays. A careful study of 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 63 



this figure will show that the gradation of shading is the reverse 
of that represented in Fig. 59 where the convex surface of the 
cylinder was exposed to view. Since the concave surface, Fig. 61, 
Hes almost wholly within the shadow, the line of greatest shadow 
will be where the arrow in the top view is tangent to the arc. 
The brilliant line is at c where the light would be reflected directly 
into the eye. 

The Cone. — A cone may be shaded by following the same rules 
of shading that apply to the cylinder, except that all the hne 
elements will converge toward the apex of the cone. The line 
shading of a cone is represented in Fig. 62. 



^^ 



^ 




V/ 


/ 




Xy 


^ 




1/ 


/ 




1/ 


/ 




WJ 


/ 




\/ 


/ 




Vy 


/ 


1 


\/ 


< 


L- 


Vi 




Fig. 61. — Line shad- Fig. 62. — Line shad- 

ing of section of hollow ing of cone, 
cylinder. 



Fig. 63.— Method of 
determining the shad- 
ing of a sphere. 



The Sphere. — The determination of the shading of a sphere is 
represented in Fig. 63. The front and top views together with 
the projections of the conventional light rays are shown. If 
the two axes ef and gh in the front view are drawn at angles of 
45°, it will be noticed that the half of the sphere above gh will be 
exposed to the light while the half of the sphere below it will lie 
in the shadow. 

The Brilliant Point. — ^In the case of the sphere, the lightest and 
the darkest parts will be points, rather than lines. Consequently, 
the hrilliant point on the illuminated half of the sphere, and the 
darkest point on the darkened half, will lie somewhere along 



64 



ADVANCED SHOP DRAWING 



the axis ef in the front view, since the light arrows at either end 
of this axis are normal to the circle at those points. In the top 
view^ it will be seen that the arrow at c locates the point in that 
view which reflects the greatest amount of light to the eye. Its 
projection on ef of the front view locates m as the brilliant 
point. In like manner d, determining the darkest point in the 
top view, projected upon ef, gives w as the darkest point in the 
front view. Above the axis gh, the shading will increase in depth 
on each side of the line ef. Below the same axis, the shading 
will decrease in depth on each side >of the line ef. 



y//////////y////77A 



CYLINDER 



SECTION OF CYLINDER 




SPHERE 




SECTION OF SPHERE 





RING 



HOOK 



Fig. 64. — Illustrations of line shading. 



The following simple method of shading a sphere, as illustrated 
in Fig. 64, is commonly used. After drawing the circumference, 
the brilliant point and the darkest point are located on the 45° 
axis. A small circle, enclosing the high light area, may then be 
lightly described about the brilliant point with the bow pencil. 
None of the shaded circles should be drawn within this area. 
This small circle should be erased from the finished drawing. 
The line shading is graded along the 45° axis as was done in 
the case of the cylinder. The line shading consists of a series of 
concentric shaded circles having the same common center as the 
center of the sphere. 

Figure 64 shows some good examples of line shading on simple 
objects. It will be noticed that the shade lines on these objects 



ISOMETRIC, CABINET, AND SHADED DRAWINGS 65 




Fig. 65. — Illustrations of line shading on some simple shop objects. 




UNIVEIPSAL COUPLING 

f^OR I" SHAFT 

Fig. 66. — Universal coupling. 



66 ADVANCED SHOP DRAWING 

are used sparingly. The draftsman should endeavor, as far as 
possible, to do line shading in a like manner. 

Some examples of line shading, as applied to simple shop 
objects, are shown in Fig. 65. Additional examples may be found 
in industrial magazines which contain many examples of this 
class of work. 

Problem 12 

Make a complete isometric drawing of the universal coupling shown in 
assembly in the freehand sketch, Fig. 66. The isometric drawing should 
be full size, but no dimensions should be shown. The drawing paper should 
be placed on the board with its long dimension horizontal, and the coupling 
drawn with the axes of the shafts lying on the 30° isometric axis which 
extends upward toward the right. The ends of the shafts should be shown 
as broken off with uneven outlines. 

Problem 13 

Make a cabinet drawing of some simple object of rectangular outline, 
such as a mission bookcase, chair, or table. No dimensions should be shown. 

Problem 14 

Make a tracing of the isometric drawing of the universal coupling which 
constituted Problem 12. Practice shading this tracing in pencil with line 
shading. When it appears satisfactory, ink it in. The ends of the shafts 
should be shown broken off irregularly. 



CHAPTER V 
PATENT OFFICE DRAWINGS 

33. Application. — ^The rules governing the application for, 
and issuance of, patents are very rigid. The Patent Office issues 
a pamphlet called the ^' Rules of Practice" which gives complete 
information covering these points. These rules are issued gratui- 
tously upon application to the Commissioner of Patents, Wash- 
ington, D. C. 

Although all matters governing the application should be left 
in the hands of a thoroughly competent patent attorney, they 
should be at least understood by the inventor. There are six 
parts to a complete application for a patent on an invention. 
These parts are: petition, power of attorney, specification, claims, 
oath, and drawings or models. 

The petition is merely a communication to the Commissioner 
of Patents, asking for a grant of a patent upon the invention. The 
petition contains information concernin<g the citizenship of the 
applicant, his address, and residence. All papers should con- 
form as nearly as possible to the forms laid out by the Patent 
Office. 

The power of attorney grants the person to whom it is given 
the power to handle the application, amend it or alter it, and 
receive the patent if it is issued. This person may not be an 
attorney, but he must be a registered solicitor of patents. While 
this power lis in force the attorney has sole control of the applica- 
tion. The power of attorney may be recalled at any time and 
another attorney be assigned the position. 

The specification is a written description of the invention to 
be patented. Its proper wording is of the greatest importance in 
protecting the inventor against infringements of similar inven- 
tion,s during the period of seventeen years that the patentee is 
privileged to enjoy a monopoly on the invention which he has 
patented. The specification should, therefore, be very broad 
and general in its scope so as to cover all infringements com- 
pletely. Only a competent and thoroughly reliable patent attor- 

67 



68 ADVANCED SHOP DRAWING 

ney should be engaged to draw up the specification. It should 
include a preamble, a general statement covering the object 
and nature of the invention, a detailed description of the object, 
the claims, and the signatures of the inventor and two witnesses. 

The claim is really a part of the specification, but it is of such 
paramount importance that some attorneys consider it sepa- 
rately. To quote from the '' Rules of Practice" '^he shall explain 
the principle thereof, and the best mode in which he has contem- 
plated applying that principle, so as to distinguish it from other 
inventions; and he shall particularly point out and distinctly 
claim the part, improvement, or combination which he claims as 
his invention or discovery." 

The claim should clearly define the limits of the machine. 
In case of litigation the courts may be lenient in regard to the 
specification but not so with the claim if it is not clear. A com- 
petent attorney should always be employed to write the claim. 

The oath is fully explained in the statute. This statute also 
prescribes what the applicant shall swear to in order that he may 
secure the patent. No chances should be taken with the oath. 

The drawings form such an important part of the specification 
that they will be considered separately in Article 35. 

34. Examination. — After the application has been filed, it is 
subject to a most thorough examination. The examination is 
particularly searching as to the novelty of the invention. This 
must necessarily be so in order to establish its priority. In the 
examination even errors made on the typewriter are noted, and 
stated in action; nothing is taken for granted. The examiner 
may reject any part of the claim as being too broad or not clearly 
stated. The applicant has a year in which to amend the 
application. 

After the application has passed the office, a formal notice of 
allowance is sent to the attorney. Six months is allowed in which 
to pay the final fee. If not paid within that time, the applica- 
tion forfeits for non-payment of final fee. 

35. Drawing. — In the case of a machine or other manufactured 
article, or whenever the nature of the invention admits of it, the 
applicant is required to submit, with the specification, a drawing 
which will clearly show every feature of the invention for which 
the patent is desired. This drawing must be in strict conformity 
to the Patent Office rules. If the invention is merely an 
improvement on an existing machine, the drawing must show 



PATENT OFFICE DRAWINGS 69 

the invention separately, and another view must show as 
much of the existing machine, with the invention attached, as 
is necessary to give a clear idea of the practical application 
of the proposed improvement. 

The drawing must be made in black ink on a smooth white 
paper equal in thickness to three-sheet Bristol board. Two-ply 
Reynolds board is preferred by the Patent Office as prints can 
be made from it very readily. The sheets must be exactly 10'' 
X 15" with the four border lines set in one inch from the edges 
as shown in Fig. 67. The sheets should be used with the long 
dimension vertical when convenient. A space of 134" must be 
left vacant just beneath the upper border line for the insertion 
of the printed title by the Patent Office. The signature of the 
inventor and attorney should be placed in the lower right-hand 
corner of the sheet, while the signatures of two witnesses should 
be placed in the lower left-hand corner. The draftsman usually 
signs the drawing as the first witness. These signatures should all 
be within the marginal lines, but should in no instance trespass 
upon the views. The title should be Written with pencil on the 
back of the sheet. 

When the sheet is used with its long dimension horizontal, 
the space for the title is provided for at the right and the signa- 
tures appear at the left, occupying the same space and position 
within the marginal area as in the upright views, and being hori- 
zontal when the sheet is held in an upright position. All views 
on the same sheet must stand in the same direction. As many 
sheets as necessary may be used. 

Sheets with border lines and lettering printed upon them are 
quite convenient for this work and are on sale by many dealers. 
Such sheets, however, are usually made up of an inferior quality 
of paper and turn yellow with age. To avoid making tack holes 
in the drawing paper, it should be fastened to the drawing board 
with the heads of the thumb tacks only. 

Patent Office drawings are not working drawings. They are 
pictorial and descriptive rather than constructional; hence, they 
have no center lines, dimension lines, notes, or names of views. 
The drawings should be made sufficiently large to show all parts 
clearly, hut need not he drawn to scale. It is customary to draw 
the part showing the invention to an exaggerated scale so as to 
show the essential parts clearly. Unessential details need not 
be drawn accurately to scale. For instance, a section of a thin 



70 ADVANCED SHOP DRAWING 

sheet of material might appear as a single line if drawn accurately 
to scale. It should rather be drawn as a double line with cross- 
hatching between. 

Crosshatching should consist of oblique parallel lines about 
one-twentieth of an inch apart. Solid black should not be used 
except to represent insulation or rubber. The ''Rules of Prac- 
tice" give all the various conventions which are to be observed in 
making patent drawings. These embrace electrical symbols, 
symbols of color, etc. 

A drawing should always be made with the fewest lines consist- 
ent with clearness, so that the hnes will be open and not run to- 
gether when the Patent Office reduces the drawing. Shade lines 
should always be used sparingly and intelligently. 

All the teeth of gears and toothed wheels must be shown; 
also chains and sprockets. Screw threads may be represented 
by the conventional symbols. 

The drawings may be made in orthographic or by any of the 
various oblique methods of projection. The isometric system 
is used extensively. The examiner is expert in reading drawings, 
but the client, and sometimes the attorney, may not be able to 
read a drawing in orthographic projection, but a drawing in 
isometric would be quite intelligible to him. All drawings 
should be checked thoroughly for correctness and completeness, 
since they may form a valuable part of the exhibit in case of 
litigation. 

The various views of the drawing are noted ''Fig. 1," "Fig. 2," 
etc., and the various parts of the mechanism are designated by 
reference numbers or letters by which the invention is described 
in the specification. All such notations should be Ke" high so 
that they will stand reduction well. One view, generally "Fig. 
1, " is made as a comprehensive view that may be used in the Offi- 
cial Gazette as an illustration to accompany the "Claims." 

A patent office drawing of a caster is shown in Fig. 67. The 
orthographic method of projection has been used. The drawing 
is of rather open construction. This applies particularly to the 
crosshatching, the line-shading, and the numerals. Patent 
Office drawings must embrace these essential features so that 
they will stand reduction well. 

The body of this caster consists of two disks separated by a 
number of idle rollers made of solid metal. The upper disk has 
a cylindrical projection on its upper surface to fit into the socket 



PATENT OFFICE DRAWINGS 



71 



h 



lO"- 



\ft 



1 




/V<7./. 



T/C?. ^. 



W/TA/E35E5 



/NVENTOR 



SMimdOAhL, 



ATTORNEy 



Fig. 67. — Patent Office drawing of caster. 



72 



ADVANCED SHOP DRAWING 




Aftorney 



FiQ. 68. — Patent Office drawing of inserted saw tooth. 



PATENT OFFICE DRAWINGS 



73 




r/ <9. /. 



Witnesses 



I invent OK 



Affoirney 



Fig. 69. — Patent Office drawing of spiked cleat. 



74 ADVANCED SHOP DRAWING 

provided for it. On its under surface, and set in some distance 
from its outer edge, a circular flange is provided as a guide for 
the rollers. The lower disk has a projection on its lower surface 
to carry the caster wheel. On its upper surface, ^nd in line with 
its outer edge, a circular flange acts as a guide for the rollers. 
The lower disk thu^ serves as a race for the rollers. A pin pass- 
ing through the centers of both disks, and riveted at both ends, 
serves to keep the two disks in proper alignment. Three holes 
are provided in the upper disk so that the caster may be fastened 
to^the leg of a chair or table with screws if desired. These are 
inserted through the large hole which is provided for this pur- 
pose in the lower disk. 

In Fig. 68 is represented a Patent Office drawing, in isometric, 
of an inserted saw tooth. ''Fig. 1" of this sketch shows a seg- 
ment of the saw with a bit and shank in place, and the spanner 
wrench engaged with which they are turned into position by 
turning the wrench in a clockwise direction. ''Fig. 2" show3 a 
detail sketch of the bit, which is made of tool steel. It is grooved 
on the back to engage with a corresponding V ridge on the socket 
of the saw blank. The shoulder on the back of the bit gives it a 
firm set against the saw blank. "Fig. 3" shows the shank which 
secures the bit in position in the socket. It likewise has a groove 
on its outer curved surface to engage the V ridge on the socket. 
"Fig. 4" shoWs a detail sketch of the spanner wrench by means 
of which the teeth are inserted and removed. 

In connection with Fig. 68 it is well to note that the use of 
broken lines has been avoided. It is sometimes better to show 
another view of an object rather than to show broken lines. 

A Patent Office drawing of a spiked cleat for the heel of a shoe 
is represented in Fig. 69. This is a good example of a drawing 
of soft material. If follows no definite rules that may be applied 
to mechanical drawings but is on the order of a freehand sketch. 
The sketch is quite simple and so well drawn that no explanation 
of its use is necessary. It is an example of good patent drawing 
practice because of the clearness with which the idea is conveyed 
by means of a few lines. 

Problem 15 

Make a Patent Office drawing of some simple patented article which may 
be accessible. Use a 10" X 15" sheet of drawing paper and follow the 
Patent Office requirements. 



CHAPTER VI 
STRUCTURAL DRAWING 

36. Structural Drawing. — The term applied to working draw- 
ings for steel structures, such as bridges and the steel framework 
of buildings, is Structural Drawing. Structural work is made up of 
rolled steel shapes fastened together with rivets and bolts. 

The departments of an ordinary structural shop in which 
structures are designed and fabricated are : 
Estimating or computing department. 
Detailing or drafting department. 
Templet shop. 
Beam shop. 

Assembling shop for girders and trusses. 
Yard. 

37. Estimating Department. — When a steel structure is to be 
built, the engineer representing the party that is to own the 
structure prepares rules regarding the loads to be used in the 
computations, the permissible unit stresses, the quality of the 
materials, and the character of the workmanship. These rules 
are called specifications and they cannot be successfully prepared 
except by an engineer of experience. 

After the preparation of the specifications, proposals or bids 
are invited from structural companies for the manufacture and 
erection of the structure. Mention is made as to where the 
specifications can be seen and information obtained. The day 
and hour when the proposals will be opened are named. 

The estimating department computes the stresses and makes 
a stress sheet. This sheet gives the principal dimensions and 
sections, and from this an estimate is prepared of the weight of 
the material from which the amount of the bid is determined. 
If the contract is secured, the stress sheet is turned over to the 
drafting department, where the details are worked out and the 
working drawings are prepared. 

38. Drafting Department. — The first thing the draftsman gen- 
erally does when a building job comes in is to find out what 
material is required and how much of it. If the structure is of 
considerable size, this is best done by laying out the work in a 

75 



76 ADVANCED SHOP DRAWING 

general way on thick browii paper prepared for this purpose. The 
details are not put in but enough progress is made to enable the 
draftsman to determine quite closely the lengths and sizes of 
the angles and plates. The list of material in stock is then con- 
sulted, and, if any material is found in this bill that is not in 
stock, a mill bill is made out. From this bill the material is 
ordered immediately from the mill by the purchasing department, 
for it must be on hand as soon as the drawings are finished. 

Shop drawings are then made. If the amount of the contract 
warrants it, several men, constituting what may be called a 
squad, are placed under a checker or squad leader, who is said 
to have charge of the job in question. 

After the drawings have been completed, shop bills are pre- 
pared. A shop bill is made out for each sheet of details. It 
should include the exact length of all material necessary to 
manufacture the members shown. A shop bill sometimes 
appears on the right-hand side of the drawing. When written 
on special forms, it should be written so that each sheet can have 
its own bill attached if so desired. One page of shop bills should 
not contain bills for two sheets of drawings. The shop bills 
serve as a guide for laying out and assembling the work. The 
items should be so grouped as to facilitate these operations. 
When shipping lists are made, the shipping mark of every sepa- 
rate assembled piece should be given, and, usually for indentifica- 
tion, the material and length of the principal shapes. 

A separate bill is made of all pieces which require forging. 
These include eye-bars, ties, and counters. Full dimensions 
and details, and perhaps sketches, are required on this sheet, 
which then goes to the forge shop. 

Riveting Conventions. — Some of the riveting is done in the 
shop and some is done in the field, or at the place where the job 
is being erected. Working drawings must distinguish between 
shop rivets and field rivets. Field connections may be made 
either by means of rivets or by bolts. Holes for field connections 
are always shown solid black. 

Many types of riveting are used in structural work, and it is 
desirable to have standard conventions for representing each. 
When such conventions are used, a key is sometimes shown on 
the drawing. The Osborn symbols of riveting, shown in Fig. 70, 
are so universally used that no key is necessary when they are 
employed on a drawing. The upper sketch of this figure shows 



STRUCTURAL DRAWING 



11 



the conventions for shop rivets, and the lower sketch shows the 
conventions for field rivets in plan. The central view shows the 
corresponding rivets in elevation. It will be noticed that the 



Plejin 



3hop F?ivet3 



Counfej'Aunk Sr 



Chipp»d 



^ 10 k (0 ^(0 



Counferaunk ^ 



Chipped -g high 



II 



^ •5 ,0 •< 






F/atfa.ned 



high 



^<0 









Flattened 



Is V"^ ^^ 

^(?5 k>n CQwi 



0-Q^-&^-^^-^^-^^^^^ 



^ 



Tzrnz. 



zti ^ J=, (^ r^r-. J-p Ar\ r\-\ r\-^ 



vi///////r^i;^^^/'^AyJ^^^^^^ 



Field R'ivets 




F'/ain i^Counter&unk &■ Countersunk A- 



Chipped 

S^ h^ ^^ 
^ m k (O ^^ 



Chipped ■§ high 



F/attensd 



X high 

^"5 ^^ ^^ 
^(0 k<o OQv) 



F/attened 



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\% \% |l 

< (0 ^v) c^(n 



Fig. 70. — Osborn riveting symbols. 



CM 



^cU 



yf 



VS3, 




5 

i 



§ 



Fig. 71. — Forms of rivets — button head and countersunk. 



conventions for shop and field rivets are the same except for the 
fact that all field rivet conventions have a solid black core. 

Figure 71 shows the general proportions of buttonhead and 
countersunk rivets. It is unnecessary to specify the lengths of 
rivets on working drawings. 



78 ADVANCED SHOP DRAWING 

Structural Line Conventions. — The principles of structural be- 
cause of drawing are the same as those of mechanical drawing. 
However, the fact that there are so many parallel lines drawn 
closely together, it is customary to use a finer line than is used 
in mechanical drawing. To avoid confusion on tracings, center 
lines and dimension lines are sometimes shown in red ink. 
Shade lines are never used. 

Dimensions. — On account of the uniformity of the spacing 
of the rivets and the small space permitted for the insertion of the 
intervening distances between them, it is customary to show the 
over-all dimension line and to note on it the distance between 
the successive rivets, the number of such spaces, and the over-all 
dimensions thus: 

49 spaces @ 4'' - 16' - 4'' 

Because of the small space usually allowed for the insertion of 
dimensions, it is customary to make numerals higher and nar- 
rower than is the practice in mechanical drawing. Dimensions 
over one foot are always given in feet and inches. 

UPPER CASE 

ABCDEFGHUnLMN 
0PQR5TUVWXYZ 

LOWER CASE 



abcdefghijh/mnopqrstuvwxyz 

I 12 I 23 II 2 I 2 1/^2 

/c (O) <m lb HJi ^n 



^»*o 



NUMERALS 

1234567890 

Fig. 72. — Form of lettering for structural drawing. 

Structural Lettering. — Figure 72 shows conventional forms, to- 
gether with the order of strokes, of the inclined Gothic type of 
lower case (small) letters which are universally used on structural 
drawings. Some such rapid type of lettering is necessitated by 
the great number of notes that is used in this branch of drawing. 



STRUCTURAL DRAWING 79 

The upper case {capitals) type of lettering is used for all plate 
titles, however. 

Material. — In all structural design work the draftsman must 
be careful to specify commercial sizes of material. These may 
be found in any handbook such as a ''Carnegie" or ''Cambria." 
These books may be procured at a shght cost and are sometimes 
furnished free of charge to draftsmen and engineers holding 
responsible positions. If such a handbook is accessible, it should 
be examined carefully. It will be noticed that for each standard 
size of material, forms of various weights per foot are listed. 
The tables also give full information concerning the strengths 
of the various standard forms. The lightest weight of each form 
is the one most commonly carried in stock by the dealers and is, 
therefore, the one which the draftsman should specify when the 
work will permit. The conditions of the problem sometimes 
make it necessary to use a heavier form. 

Bent plates and bars should be developed so that their stretch- 
out dimensions may be shown. 

The stress diagram is sometimes added to the drawing. It 
shows the result of the draftsman's computations in a graphical 
manner. From it the sizes of the various members necessary 
to withstand the strains put upon them are determined. 

A hill of material of some form or other always accompanies a 
working drawing. It is sometimes placed on the drawing itself, 
although it is now considered the best practice to attach it as a 
separate hill sheet. Such a bill of material shows the designating 
mark of each piece, its size, weight per foot, over-all length, 
the number of pieces required, etc. This makes it possible for 
the office to order, at a moment's notice, whatever material may 
be necessary for a job. 

39. Examples of Structural Drawings. — Figure 73 shows a 
conventional working drawing of the lower part of a channel 
column for a building. It is a "built-up" column consisting of 
two 10'' channels spaced 6'' apart by means of two "web plates." 
The broken outlines show^ the positions of adjoining members 
in the completed structure. They are shown here merely by 
way of illustration and would not be shown on a working drawing. 

A splice connection occurs just above the first floor. Splice 
plates attached to the web plates of the column, and angles at- 
tached to the webs of the 10'' channels, form a stiff joint for both 
sections of the column, and the bearing place interposed between 



80 



ADVANCED SHOP DRAWING 




3ec//o/7 A- A 

Afafr/af in b^SB 
I PI. 22^'Kf^xZ''0''(') 
ZP/i. //£k ^'%2-<r(2) 

Mak£: /Column. Marh Ct. 



Fig. 73. — Working drawing of lower part of channel column. 



STRUCTURAL DRAWING 



81 



gives an even distribution of load from the upper to the lower 
section. The blackened holes indicate the riveting which must 
be done in the field; that is, when the work is erected in place. 
It will be noticed that the column has a built-up base which 
gives a large bearing area. The base of the column is milled 
before the base plate is put on so as to give an even distribution of 
load. The upper end of the column is hkewise milled so as to 



f eiRDCBS LIKE THIS 

W\AnnA\ A2.A3 A4 



Bill of Material for 4 girders 


Item 


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STIFF U 


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THRO'CfMTEfJ 



Rivets ^' 
Open Holes J| 
r*ikt onc (.oat 
Red lead. 



Fig. 74. — Shop drawing of girder. 



give an even bearing for the bearing plate. The four black holes 
in the base plate are for the anchor bolts by means of which the 
column is secured to the foundation. The rivets of the base 
plate are countersunk on the lower surface so as to give a smooth 
surface. This face is shown by the conventional symbols. 

At the first floor level the floor beams in one direction consist 
of two 10''-25 lb. I-beams, while in a direction at right angles to 
this they consist of single 8''-18 lb. I-beams. These I-beams are 
fastened to the column by means of bolts. Notice should be taken 
how the ''out-standing" dimensions of the bolt holes for the 8" 

6 



82 



ADVANCED SHOP DRAWING 




6 



STRUCTURAL DRAWING 83 

I-beam supports are shown. The abbreviation ''o.s." means 
"out-standing." The '^gage" of an angle is the distance from 
the back of the angle to the line of rivets. By means of the 
view at the right it will be seen that the two "L's" 3>^'' X W2' 
X Ke'' are secured to the column by means of two "through 
bolts." The two "L's" 6" X 6'' X VW are bolted to the 
flanges of the two 10" channels. The number in parenthesis, 
following the size of a member, is the number of members of 
that exact type that is required for one complete column. 

Upon close examination it will be seen that that part of the 
drawing affected by the notation "42 spaces® 4" = 14' — 0"" 
is not drawn to scale because it is of uniform section throughout. 

Figure 74 shows a shop drawing of a girder. The girder is 
symmetrical about its center line so that it is necessary to 
show a drawing of only half of it. The detailed information as 
to the materials required is listed as a separate bill of material. 

This girder consists of a plate "v^ith pairs of flange angles at the 
top and bottom reinforced by web plates. Other plates called 
cover plates are shown outside of the web plates. The main plate 
of the girder is reinforced with angles called stiffeners. Fillers 
are used betw;,een the stiffeners and the plate so that it will not 
be necessary to crimp the stiffeners around the web angles. It 
will be noticed how the section through the center is shown. 
Instead of showing the bottom view, it is better practice to show 
a section taken through the girder looking down upon the lower 
flange angles. 

Figure 75 shows a working drawing of a roof truss. Because 
of its symmetry about the center line, only half of the truss is 
shown. A marking diagram is attached and the drawing is 
marked to conform to it. It should be noticed how the inclina- 
tion of the various members is noted by their tangents on a 12" 
base line. It is unnecessary to draw the 12" base line to scale. 

40. Templet Shop. — ^After the shop drawings are made, 
checked, and approved, they are blue printed and sent into the 
templet shop. 

For small and general work each templet is made separately 
from the detailed shop drawings. A templet is either a board or 
framework of boards, the plane of one of its sides being an exact 
representation of the plane of one of the sides of the metal shape 
or piece which is to be made. Holes are bored in the wood at 
all points where rivets are to be driven. This templet is then 



84 ADVANCED SHOP DRAWING 

clamped upon the piece, and the positions of the holes, bevels, 
and notches are marked upon the metal face. 

41. Beam Shop. — The work on beams and channels is carried 
on in what is called a beam shop. In case the material has been 
shipped from the mill according to the mill bill made out in the 
drafting room, the beams are found in that portion of the stock 
yard reserved for the job in question. If the material is to be 
taken from stock, the proper lengths are cut from stock lengths 
with a cold saw* or beam shear, which is usually located in the 
stock yard. In the beam shop the templet is laid on the beam 
and the positions of the holes, bevels, and notches are marked 
upon the metal. The centers of the holes are marked with a 
center punch w.hich exactly fits the holes in the templet. The 
position of each hole is thus indicated by a small indentation in 
the metal. The bevel and notch lines are drawn on the metal by 
scratching or marking with chalk along the edges of the templet. 

The beam is then taken to the power punches where the holes 
are punched. If there is any special cutting or bending to be 
done, it is performed before the piece is taken to the riveting 
machine to have connections riveted on. The beam is then 
taken to the end of the shop nearest the yard and the parts not 
accessible after assembling are thoroughly painted. 

42. Assembling Shop. — In this shop all the material is brought 
together, fitted, riveted, and made of exact dimensions; when the 
members leave this shop, they are ready to be prepared for ship- 
ment. Pneumatic portable riveters are used on the heavier 
pieces of work. For columns there is an additional operation of 
planing or milling the ends of the riveted sections before the caps 
or base plates are riveted on. 

43. Yard. — After the material is finished in the shops, it is 
taken out into the yard and placed in that part of the yard 
assigned to the particular job number. It should be inspected 
carefully in order to see that it conforms in every way to the 
specifications and to the drawings. All work should be painted 
and have the approval of the company's inspector before being 
shipped. 

Problem 16 

Make a working drawing of a column similar to Fig. 73 with the following 
exceptions: 

1. Distance from back to back of the two 10"-20 lb. channels shall be 
6K" instead of 6". 



STRUCTURAL DRAWING 85 

2. Distance from milled base (or top of base plate) of column to top of 
first floor beams shall be 20' 0" instead of 18' 0". 

3. Distance from top of first floor beams to upper milled end (or bottom 
of bearing plate) of column shall be 1' 4" instead of 1' 7". 

4. The column to be for the corner of the building. This will require 
floor beams and their supports on only two sides of the column rather than 
on all four sides as shown in Fig. 73. The floor beams thus supported shall 
consist of one8"-181b. I-beam in one direction and two 10"-25 lb. I-beams 
in the other direction. This will cause changes in Fig. 73 as follows: 

1. There will be a change in the width of the web plate. 

2. There will be an increase in the number of rivets, spaced at 4", which 
fasten the web plates to the two 10"-20 lb. channels. 

3. The distance between the lower end of the splice plate and the upper 
angle to which the two 10 "-25 lb. I-beams are bolted will be decreased 
by 3". 

4. Angles for the support of the floor beams will be needed on only two 
sides of the column. Through bolts will still be needed for fastening the 
33-^" X 33^" X Ke" *'L" to the column, because of the inaccessibility of 
the rear side of the web of 10" channel to which it is attached. 



CHAPTER VII 

ELECTRICAL DRAWING 

44. Electrical Drawing. — Electrical drawing, like mechanical 
drawing, includes several specialized lines. Since the drafting 
of electrical machines, fixtures, and appliances is so much like 
mechanical drafting, this chapter will deal only with wiring dia- 
grams which illustrate electrical drawing in a specialized form. 



m Main or Feeder run Concealed under F loor 

• """" " " ' a\>o\ie 

- Branch Circuit run Concealed under Floor 

_ . • •. • MX obovc 

- • . n Expoeed 



rO- 



KXKKXXJtXi 



Lamp Circut ( Arc) 



— • •—Pole tine 

I Riser 



-4^ Crossing Wires 



(2i 



Joined Wires 



©Ceiling Outlet .Electric only. Numeral in centfer 
indicotes number of Standard 16 CP Incandescent Lamf)s. 

r^ Drop Cord Outlet 



-(")- Chandelier Inc^jndcsccnt Lamps 
O 5P Switch Outlet 

S^ D.P. •• •• 

S 3- Way " 

Q Meter Outlet 
HBH Distribution Parxl 

Junction or Pull Box 



-o- 

-O 
-O- 



-O- 

-o- 
-o- 



Lamp Circuits (Incandescent) 

( t j Galvanometer ~^WVWWW Resisfance 

rAj Ammeter — ^Wft^ ' — Variable Resistance 



— |«|ill|i|iH ®«««'-y 



Bell 



E-sJ — Buzxer 

III 



1^ 



Condenser 




A.C Generator (Single Phase) 
'T j^ D. C. Qencnatw 




Am meter 
Voltmeter 
Wot t meter 
Meter 

Transformer 
Rotary Trans|brmcr 

Motor 




Phcostat 



Knife Switch 



Fuse 



Lightning Arrester 



Ground 



Fig. 76. — Table of electrical symbols. 

45. Symbols. — In electrical drawing, as in various other highly 
specialized branches, the draftsman has constant recourse to 
standard symbols by which the various appliances are desig- 

86 




ELECTRICAL DRAWING 87 

nated. Figure 76 shows the most generally recognized symbols 
for the more common electrical devices. Many of these are 
taken from the Hst of standard wiring symbols adopted and copy- 
righted by the National Electrical Contractors' Association and 
the American Institute of Architects. Others are taken from 
the ^' Rules of Practice" of the United States Patent Office. 
These symbols are so generally used in practice that it is not 
necessary to show a table or ''key" of them on the drawings. 

46. Wire Size. — Wire is usually sold by ''gage numbers," 
that is to say, manufacturers employ certain arbitrary numbers 
to indicate wires having various diame- 
ters. Figure 77 shows an American 
standard wire gage. Different slots on 
the gage should be tried on the wire 
until one is found which will just fit 
over the wire. The number of that 
slot is the gage number of the wire. 
The circular mil is another term em- 
ployed in dealing with wire sizes. The 
word mil means one-thousandths of ^ „^ , . , , , 

. . Fig. 77. — American standard 

an inch. A wire having a diameter of wire gage. 

.001 in. is said to have an area of one 

circular mil. The diameter of any wire expressed in mils is the 
diameter in one-thousandths of an inch with the decimal point 
removed. The area of any wire in circular mils is the square of 
the diameter in mils. This system of measurement is used mostly 
for wires of large diameter. After the size No. 0000 is reached, 
the area of the wire is usually expressed in circular mils as: 
200,000, 300,000, etc. up to 2,000,000. 

47. Bell Circuits. — Figure 78-A shows a simple bell circuit 
such as might serve for a doorbell. Power is supplied by a 
battery or dry cell. It should be noticed that one side of the 
battery is connected directly to one terminal of the bell. The 
other side of the battery is connected to the button, and then 
the button directly to the other terminal of the bell. Completing 
the circuit by a push on the button causes the bell to ring. In 
the symbol for a battery, each pair of lines represents a cell. 

Figure 78-5 shows a bell controlled by two push buttons. It 
should be understood that in order to ring a bell from either of 
two buttons, the circuit must be completed by pushing either 
button. This is done by connecting the two buttons in parallel, 



88 



ADVANCED SHOP DRAWING 



tons in parallel, or, in other words, an uninterrupted connection 
must be run from the battery to each button. The same must 
be true of the connections from the buttons to the bell. As 
before, one side of the battery is connected directly to the bell 
and the other side through both buttons to the bell. It can be 
seen from the figure that a complete circuit is established when 
either of the buttons is pushed. 

Figure 78-C shows an arrangement by which two bells may be 
rung simultaneously from a single push button. In this case it 






Fig. 78. — Simple bell circuits. 



should be noticed that the two bells are in parallel. One side 
of the battery is connected directly to each of the two bells. The 
other side of the battery goes to the button and there a direct 
connection is made to each of the bells. It may be seen that 
with this arrangement, when the button is pushed, the current 
has an uninterrupted connection to each bell and so causes them 
both to ring. 

Figure 79 shows connections for one bell and an indicator for 
several stations. Such an arrangement as this is widely used 
in hotel and elevator service. In a hotel the indicator would be 
located near the clerk's desk and the buttons in the various rooms. 



ELECTRICAL DRAWING 



89 



It should be noticed that as before the bell is connected directly 
to one side of the battery. The other side of the battery con- 
nects directly to each of the buttons. From the buttons the cur- 



d 



t 



I 



66666 









Fig. 79. — Bell and indicator circuit. 

rent flows through the indicator, to the other side of the bell. 

The indicator is merely a set of coils wound around small metal 

cores. When the current flows 

through the coil, it magnetizes 

the core. This magnetized 

core attracts the indicator 

needle. The core retains 

enough magnetism to hold 

the needle against it until 

freed by a slight jar. 

Figure 80 shows an apart- 
ment house arrangement 
whereby a call may be made 
from the front door; the door 
opened from the apartment; 
and a buzzer or bell rung 
from the apartment door. 

48. Two-wire Circuits. — 
The simple two-wire system 
is a method of distribution 
very largely used, particularly 
in small isolated plants or 




jL/DOOR 



PEINER. 



where the power is not car- ItIt 



ried to great distances. The Fig. SO.-Bell system for apartment house. 

lamps are usually operated at 

110 or 220 volts. Figure 81 shows such a system. The 

switches, fuses, and other accessories are omitted for the sake 



90 



ADVANCED SHOP DRAWING 



of simplicity. The sketch shows the two mains A-A running 
from the generator. Branch mains or laterals may be con- 
nected to the mains at any point. Where the mains are of any 
considerable length, they are usually designated as ^'feeders." 
In electrical drawing, when two wires cross, but do not inter- 




■o 
o- 
-o 



o 



^^^6^i> 



7J 



o 
o 
o 
o 



<y 

o 
o 
o 



o 
o 
o 
o 
o 



Fig. 81. — Two-wire lighting circuit. 



f <?<?<?<? 



(><><><>(><;><> 



sect, one of the lines is crooked in the form of a semi-circle at 
the point of crossing. When two intersecting lines indicate 
wires that are connected at the point of crossing, that fact is 
denoted by a dot at the point of intersection. 

It should be noticed that all the lamps are put in in parallel 
and not in series. In other words, any one lamp may or may not 




o- 

o 
o- 
o 
o 



^^^^ 



-0--0- 
-0--0 

■o-o 



JMM 



o-o 
o-o- 
-oo- 
oo 

oo 



-o 
-o- 
-o- 
-o- 
-o- 
-o- 



m 



Fig. 82. — Three-wire lighting circuit. 

burn, without interfering in the least with the operation of tne 
other lamps. In a series circuit, if one lamp goes out, the cir- 
cuit will be broken and all the lamps will go out. 

49. Three -wire Circuits. — The three- wire system, as illustrated 
in Fig. 82, is used a great deal at the present time. In such 



ELECTRICAL DRAWING 



91 



a system two wires, A and B, supply the power. The return main 
for both of these wires is C. 

These circuits are used mainly in public buildings where some 
of the feeders must necessarily be long and where the load may 




Fig. 83. — Three-wire circuit with storage battery auxiliaries. 

be quite heavy. When wires are heavily loaded by attaching a 
great many lamps, the drop in voltage through the circuit may be 
so great as to cause the lamps to burn dim. This difficulty may 



^ <!> <^ 6 



«-B<fiMI 



3ZOZII 



4- 



l^ITXT 



^ 



'OO-a-ete t r — r T- 



a 



3za~ii 



^ 



^ 



II=5zo: 



±±^ IM z^ 



o-^ 



H^ 



-6^ 



a 



f ? I 

Fig. 84. — Three-wire system with one main distribution center and three smaller 

panels. 

be largely oiffset by increasing the voltage. In a three-wire cir- 
cuit the voltage across the two wires A and B is 220 volts. The 
voltage from A to C and from 5 to C is 110 volts which is the 
usual voltage used in lighting circuits. Thus by connecting 
lamps across from A to C they are operated at 110 volts although 
the feeders carry 220 volts. 



92 



ADVANCED SHOP DRAWING 



Another advantage in the three-wire system is that it renders 
the same service as two complete two-wire circuits and saves 
one wire. 

Figure 83 shows such a combination with a storage battery in 
each of the mains to provide for any fluctuations of the load. It 
often happens in three-wire circuits that one side of the circuit 



220 VOLT MOTOR 



220 VOLT MOTOR HME 



220 



CUT 
007 



VOLT MOTOR LINE 




"I 



lO H-P. 



220 VOLT MOTOR 






o-io 
00 
00 



CENTER OrD»STR»BUT»ON <><> 




Fig. 85. — Three-wire power and lighting circuit. 

is more heavily loaded than the other. These storage batteries 
placed in the line tend to balance the pull on the generator. 

Figure 84 shows a three-wire system with one main distribution 
center and three smaller panels. Sometimes the three service 
wires run only to the main distribution panel and the other 
feeders are run on two- wire circuits. 

Figure 85 shows another example of the same system where 
current is used for illuminating purposes and also for operating 
two motors. Two centers of distribution are shown here. It 



ELECTRICAL DRAWING 



93 



should be noticed that the motors are run from the two outside 
feeder wires. This means that they are 220- volt motors. 

50. Wiring Diagrams. — Interior weiring diagrams are usually 
not necessary for electrical installations in residences and small 
factories. Verbal or written instructions are often sufficient. 
Usually the blue prints of the floor plans show the approximate 
location of lights and switches as well as the meter board and 
distribution panel. The location of the risers and feeders is 
left to the electrical contractor. Wiring diagrams are necessary, 
however, for elaborate systems such as are to be found in large 
office buildings or hotels. 



MAIN CUTOUT, METEF?, ETC. 
IN CORNIER OF BASEMEMT. 




CHAMBER 96* 10 O 




5ECOND FLOOR PLAN. 



FIRST FLOOR PLAN. 

Fig. 86. — Wiring diagrams for cottage. 

Figure 86 shows typical wiring diagrams for the two floors of 
a cottage. The branches are usually strung under the floors and 
the risers concealed in the walls. 

Figure 87 and Fig. 88 show some typical wiring diagrams to- 
gether with a key of the symbols used, taken from catalogs of 
the General Electric Company. These diagrams give complete 
information to the electrician so that the system may be installed 
and wired without particular difficulty. 

Figure 89 shows a six-circuit panel with fuses such as is listed in 
the General Electric catalog. The first sketch shows the front 
of the panel giving the location of the switches and meters; the 
second sketch shows the wire sockets on the rear of the panel for 
the reception of the wires; the third sketch shows the wiring 



94 



ADVANCED SHOP DRAWING 



,>-Ay\rsA/^^ 



(.-^vV^A^^ 



•*■ eus 



-P'oHj 



/ 



CIRCUIT 
BREAKER 




AMMETER 
SHUNT 

|go} -Q 



X 



o— fooj f-A/VNAA^ 

OVERLOAD 
COIL 




± BUS 



COMPENSATOR 



o— loot- 



= BUS 



X 
GENERATOR 



SERIES 

riELD 



eus- 



BUS- 




A.Mi= Ammeter. 
B.A.5.=Bell Alarm Switch. 
C. ^Compensator. 
C.B. =^CiRcuiT Breaker. 
C.C. =CoNSTANT Current 

Transformer. 
C.H. -Card Holder. 
C.T =CuRRENT Transformer 
D.R =DiscHAR6E Resistance. 
F. = Fuse. 
F. 5. = Field Switch 
G.L. =Ground Detector 

Lamp. 
LA. =Li<iHTNiNG Arrester. 
N.P =Name Plate. 

0.C.=0VERL0AD CojL. 

O. S. = OiL Switch. 
P.P. =PoTENTiAL Plug. 
PR. -Potential Receptacu. 
P.T. =PoTENTiAL Transformer. 
R. =Rheostat. 
P.M. =Handwheel for 

Rheostat Feeder. 
S.8'5i=Plug Switch. 
SH. =5hunt. 
T C.=OiL Switch 
Trip Coiu. 
V. =Volt Meter. 



Fig. 



3- Wire 
Qeneratoc 



87. — Wiring diagram from General Electric 

to symbols. 



Co. catalog, giving key 



ELECTRICAL DRAWING 



95 



diagram for the back of the panel. The drawings of the fronts 
of the panels are generally made according to the general prin- 
ciples of orthographic projection; that is, the various electrical 






Al 

' ) c.c. 



FEEDER 

ljpj| 



FEEDER 






RR. 




qOOO 



i)—j\ 




Al )l a! )( Al 



oo 



P.P. 



F 



RT. 



F.S. 



P.R. 




tt 



EXCITER A.C.qENETRATOR 

Fig. 88. — Typical wiring diagram from General Electric Co. catalog. - 

devices are shown in approximate outline. No attempt is made 
at exact representation. 

In Fig. 90 is shown a lightning arrester house with ground con- 



96 



ADVANCED SHOP DRAWING 



-OCXrO-^ 





+ « 




i 



I 

00 

d 



(—^ 




>-n-B-a&Ozl}fl 



s-asQ i&a 



Lte=aeCl=0^ 



s=asa=t)a 



=aecncia 






s=aeO=l}^ 



l)=g=a&Q=Da 



:D= 



:d: 



ELECTRICAL DRAWING 



97 



nection. The current flows from the Hne, through the choke 
coil and switch, out to the mill. The hghtning arrester consists 
of the choke coil and the series of gaps in the ground line. The 
choke coil has no appreciable effect on current of ordinary fre- 
quency and voltage, hence it offers no resistance to the power cur- 
rent. Lightning, however, is a current of extremely high fre- 




QROi/NO WIRE AT 
'least no. 6 B4S 



WIRE SOLOCREO TO BRASS 
SCREWED TIGHTLY INTO 






CRUSHED COKE 
OB CHARCOAL.-- 
PEA Size . , ' ^ 

//^ //^ //Y //,%/ 



J^:.-..<,.'..V''ao V 









7. 

?Q(iOUND WIRE RIVETED IN A NUMBER OF PLACES TO 

:oL0 



JCOPPER PLATE, AND 





t 



mwr/m 



SOLDERED roP. WHOLE 
ISTANCE ACROSS. 

NO. IS QAuaC COPPER PLATE 
ABOUT 3X6 FEET, AT LCVCL OF 
PCRMANEWTt.r DAMP EARTH. 



Fig. 90. — Lightning arrester house showing connections. 

quency and voltage. When it strikes the hne and attempts to 
flow through the choke coil, the coil builds up a counter voltage 
which checks the flow. On account of the high pressure the cur- 
rent jumps the gaps and is led off to the ground where it is 
dissipated. 

Problem 17 

Figure 91, Fig. 92, and Fig. 93 are rough electrical sketches. Work these 
up into neat drawings and supply the missing symbols. 



98 



ADVANCED SHOP DRAWING 



If^ TJ^y.^ 



j(^ p:x.^ 







Fig. 91. — Bell wiring diagram for four-flat building. 



^^}^»/iU44jL. ^ « litK uAA^ 



P^ 



Ayyi/tnitX^ 




Fig. 92. — Connections for measuring transformer losses during impedance test. 



ELECTRICAL DRAWING 



99 



n'^- 




Fig. 93.— Connection for electric lighting system with compound wound 

generator. 



CHAPTER VIII 
PLANS FOR PIPE SYSTEMS 

51. Pipe. — There are several kinds of pipe commonly used 
in industry; as wrought iron, cast-iron, steel, lead, and brass 
pipe. Wrought iron pipe is the most commonly used. It is 
used for plumbing and heating purposes. Conduit for electric 
wiring purposes is the cheapest grade of wrought iron, lacquered 
both inside and outside to reduce the roughness. Cast-iron pipe 
is usually used in the larger sizes for water mains or underground 
systems. Boiler tubes are usually made of steel. A great deal 
depends on the quality of a boiler tube. There must be no weak 
places in it and it must be strong to withstand the pressures it is 
subjected to. Lead pipe is sometimes used for connecting plumb- 
ing fixtures to drains. In the smaller sizes it may be easily bent 
with the hands. This makes it easier to make a joint in difficult 
places. It is never used on supply water mains as it is liable to 
poison the water. Brass pipe is used in the smaller sizes; mainly 
as oil ducts on machinery. It is used also for hot water or pol- 
luted water since it does not corrode as iron pipe does. 

52. Pipe Sizes. — Pipe is designated by the nominal inside 
diameter, which differs slightly from the actual inside diameter 
as will be seen in Table 4. 



OO 




Standard Extra Heavy Double Extra Heavy 

Fig. 94. — Thickness of pipe. 

Pipe is manufactured in three thicknesses or weights, known 
commercially as Standard, Extra Heavy, and Double Extra Heavy. 
Standard weight pipe is used on all hot water and steam heating 
work. The heavier weights of pipe are used in high pressure 
lines. Extra heavy and double extra heavy pipe have the same 

100 



PLANS FOR PIPE SYSTEMS 



101 



outside diameters as the standard weight pipe of the same nomi- 
nal size, the added thickness being on the side. An illustration 
of these is shown in Fig. 94. 



Table 4 


— Dimensions of 


Standard Steel and Wrought Iron Pipe 


Nominal 


Actual 

outside 

diameter, 

inches 


Actual 

inside 

diameter, 

inches 


Internal 

area, 

square 

inches 


Threads 
per 
inch 


Distance 
pipe 

enters, 
inches 


Actual inside diameter 


inside 

diameter, 

inches 


Extra 
heavy, 
inches 


Double 

extra 

heavy, 

inches 


H 


0.405 


0.270 


0.057 


27 


He 


0.205 




H 


0.540 


0.364 


0.104 


18 


%2 


0.294 




H 


0.675 


0.494 


0.191 


18 


^%4. 


0.421 




>2 


0.840 


0.623 


0.304 


14 


H 


0.542 


0.244 


r4. 


1.050 


0.824 


0.533 


14 


W32 


0.736 


0.422 


1 


1.315 


1.048 


0.861 


IIH 


V2 


0.951 


0.587 


iVi 


1.660 


1.380 


1.380 


UK 


^H4. 


1.272 


0.885 


IK 


1.900 


1.611 


2.038 


UK 


%6 


1.494 


1.088 


2 


2.375 


2.067 


3.356 


UK 


»K4 


1.933 


1.491 


2>^ 


2.875 


2.468 


4.780 


8 


% 


2.315 


1.755 


3 


3.500 


3.067 


7.388 


8 


1^6 


2.892 


2.284 


3K 


4.000 


3.548 


9.887 


8 


1 


3.358 


2.716 


4 


4.500 


4.026 


12.730 


8 


iKe 


3.818 


3.136 


4K 


5.000 


4.508 


15.961 


8 


IK4 


4.280 


3.564 


5 


5.563 


5.045 


19.985 


8 


IH2 


4.813 


4.063 


6 


6.625 


6.065 


28.886 


8 


IK 


5.751 


4.875 


7 


7.625 


7.023 


38.743 


8 


IH 


6.625 


5.875 


8 


8.625 


7.982 


50.021 


8 


iKe 


7.625 


6.875 


9 


9.625 


8.937 


62 . 722 


8 


1%6 


8.625 




10 


10.750 


10.019 


78 . 822 


8 


l^Ke 


9.750 




11 


11.750 


11.000 


95.034 


8 


12^2 






12 


12.750 


12.000 


113.098 


8 


IK 


11.750 





53. Pipe Thread. — -All pipe is now threaded uniformly, the 
Briggs' standard of pipe thread sizes being used by all manufac- 
turers. The taper is an inclination of 1 in 32 to the axis, or %^" 
per foot. Figure 95 shows an enlarged view of a pipe thread 
with the relative sizes of the various parts noted. 



riat Tops 
Flat 3offoms 



-- 4- Threads —- Z Thds. 



riot Topi 

Round 
Bottoms 



Complete Ttireads 
Round Tops and Bottoms 

60. 



f Tapar ^ t>er I" of Lengftti 




.8 outside diam. -h 4'.Q 



Number of Threads f^r f 

Fig. 95. — Section of Briggs' pipe thread. 



102 



ADVANCED SHOP DRAWING 



54. Fittings. — The term fittings is applied to elbows, tees, 
crosses, unions, caps, plugs, etc. The dimensions of fittings 
vary somewhat with the different manufacturers. For this 
reason, if given at all, dimensions should be given from center to 
center of fittings. They are not usually given, however. The 
lengths of the various pipes and the arrangement of the coup- 
lings are generally left to the discretion of the pipe-fitter, though 
the drawings should always show the size of pipe. 



(Flange 



Croaa 



W^M 



i--v 

X — 



M=J 




5izeof 
Pipe 


A 


B 


c 


E 


G 


H 


K 


L 





p 


s 


T 


V 


X 


1 
8 


31 
3Z 


3 
4- 


5 
/6 


/J 


Hi 


Zl 
3Z 






1 
4- 


1 
A 










1 
A- 


'i 


29 
32 


13 
3Z 


/,-i 


zA 


25 
3Z 






3 
S 


1 
A- 










3 

a 


'i 


'k 


1 
Z 


//6 


za 


29 

3Z 


13 
/€ 


1 

A- 


3 


S 

le 










1 
2 


li 


li 


9 

16 


^3Z 


3,-4 


Ik 


/i 


1 
A- 


3 

6 


s 

16 










3 
4 


1 '^ 

'7^ 


lA 


Zl 
3Z 


2^ 

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3§i 


Ik 


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1 


7 

76 


3 

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H 


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7 
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S 

a- 


1 


7^ 


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3 

4- 


2fl 


4I 


li 


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3 

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// 
76 


7 

16 


4- 


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7 
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/I 

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li 


H 


2 


27 
32 


H 


5A 


i'& 


2 


3 
e 


3 


1 
2 


4-k 


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1 
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24 


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7S 


1 
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l-k 


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ts 


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1 — 
'32 


ii-k 


15k 


3- 

■^32 


ei 


3 

4- 


2r 


1 


II 


7^ 


/ 


li 



Table 5. 



Table 5 shows some of the common cast-iron fittings and their 
corresponding dimensions for the various sizes of pipe with which 
they are used. Table 6 shows a similar table for malleable fittings. 

Malleable fittings are used almost universally for gas piping. 
They have a smooth exterior and are of uniform section through- 



PLANS FOR PIPE SYSTEMS 



103 



Check Va/ve 




/'^o^^fig °AVy^'on 9c'sn^ 



kJ 



^'f^^^L^tlinj ^ t 

4^ 



Size of 
Pipe 


A 


B 


C 


E 


G 


H 


J 


K 


L 


N 





P 


s 


T 


1 
6 


£ 


5 

e 


1 

6 


13 
3Z 


13 
76 






3 
6 




I& 


3 
6 


li 






1 
4- 


s 


3 

A- 


3 
/G 


3 


irz 


1 


1 


3- 

e 




I& 


1 

2 


li 


7 

e 


1 
4- 


3 

8 


ih 


1 


/ 


Z9 
3Z 


If. 


1 


Ik 


s 
e 




li 


/ 
2 


li 


/ 


f6 


/ 

Z 


li 


/^ 


1 
A 


'32 


/A 


lA 


1^ 


B 




1^ 


/ 
2 


li 


li 


3 
3 


i 


li 


li 


1 
a: 


lik 


//4 


/« 


li 


7 

e 


//f 


zA 


/ 
2. 


zi 


l-k 


3 

a 


1 


zh 


1% 




If 


I'A 


/I 


z 


I7k 


li 


Zfz 


9 

/6 


zi 


fi 


7. 
/6 


li 


z-k 


/* 


3 

e 


/|^ 


zm 


li 


z 


li 


2* 


3k 


9 


2f 


^i 


/ 
2 


li 


2f 


2 


3 

a 


2i 


2« 


z 


2 


1% 


2# 


3i 


f 


Zi 


Zi 


/ 
2 


z 


H 


2i 


3 

a 


z¥. 


2* 


zi 


zh 


li 


Zi 


4n 


a 


3i 


3 


1 
2 


2i 


4 


2* 


/e 


34 


2:1 






li- 


2i 


^n 


3 


^i 


4i 


S 

e 


3 


5 


3 


1 

2 


3ii 


3h 






li 






7 
3 


3i 


^i 


3 


H 


H 


3- 


S 

a 


4ii 


3rh 






z 




6f 


•7 

e 


4i 


S 


1 


4 


ei 


4 


s 
a 


4% 


3^ 






z 




7& 


r 
e 


4i 


6i 


/ 


4i 


6i 


^i 


1 


^3Z 


3i 






Zir 










7 


/ 


5 


li 


5 


e 


ei 


4i 






zi 










7i 


/ 


6 


6i 


6 


s 
a 


7£ 


4i 






zi 










&i 


/ 



Table 6. 



out. Cast-iron fittings are used in most other branches of work. 
The sketches accompanying Table 5 show cast-iron fittings with 
a flat bead, while the malleable fittings shown in Table 6 have a 
rounded bead. 

Unless otherwise ordered, all threads of 
fittings are right-handed. If a fitting has 
both right- and left-hand threads, its ex- 
terior is ribbed as shown in Fig. 96. 

55. Piping Symbols. — Various attempts 
have been made to revolutionize piping ^i^- 96.— Right and left 

i . uxi-xix- PA- 1 malleable coupling. 

drawmg by the mtroduction of hne and 
symbol methods similar to the practice followed in electrical 
drawing. These methods have not met with universal favor, 
however, and no such set of symbols has ever been standardized. 




104 



ADVANCED SHOP DRAWING 



The universal and best practice today shows all piping, fittings, 
and apphances in their approximate outhnes. Whenever nec- 
essary, notes are attached to describe the fittings or apphances. 
56. Piping Drawings.— Figure 97 shows a conventional drawing 
of a branch tee mitre coil. Such a drawing needs no explana- 
tory notes except to specify the size of pipe. Each piece is so 
represented that no one could mistake its identity. 




Sranch Tee - Mitre Coil 



Fig. 97. 




ConnQcHon to 
£.)^panxon Tank 



fWW^ 




Fig. 98. — Two-pipe system of hot water heating. 

Figure 98 shows a general elevation of a two-pipe system of hot- 
water heating. Figure 99 is a basement plan of the system shown 
in Fig. 98. A two-pipe system has both supply and return mains, 
thus insuring a positive circulation. In a one-pipe system only 
one pipe leaves the boiler. A tap is made from the upper side 



PLANS FOR PIPE SYSTEMS 



105 



of the pipe for the supply to the radiator and the return is tapped 
into the lower side of the pipe. The connections on the radiator 
are the same as in the two-pipe system. The only saving in the 
one-pipe system is that there is only one main in the basement. 
The hot supply water flows along the upper side of the pipe and 
the cold return water on the lower side. The one-pipe system 
gives very good satisfaction in small installations. 




Fig. 99. — Basement plan of piping — two-pipe system. 




Fig. 100. — Expansion tank connection with drip — overhead system. 

It will be noticed at the top of Fig. 98 that a note appears: 
''Connection to Expansion Tank." The expansion tank is 
usually placed in the attic or above the highest radiator. Figure 
100 shows a drawing of an expansion tank with its connections. 

Figure 101 shows a very good hne drawing of part of the steam 
heating plans for a building. The steam mains are represented 



106 



ADVANCED SHOP DRAWING 



by heavy lines, the risers by lighter Hnes. A prominent numeral 
appears alongside the main between each pair of risers to show 
the size of the steam main between those two points. Valves 
are shown by an ''X" placed in the Hne. Light lines are drawn 



4-4-'''3 



36° 2 



56" I 



/i" 



fi' 

fi" 

2" 

2" 



QO"' 


4 


54-'' 


3 


60" 


2 


64-"' 


1 


4^"' 


a 



34-'" 3 



56' 



60' 



60' 



60"' 4 

iV /i' 

ir 2 - 



64' 



54' 3 



56" 



60" I 



4A'' 3 



7Z2ZZZZZZZZZZ3 




Fig. 101. — Line drawing of steam heating plan. 




Fig. 102. — Corner pipe coil. 

at right angles to the risers to represent the various floors; upon 
each is shown the number of square feet of heating surface in the 
radiator for that particular floor, followed by the letter B to 
represent the basement, or the number of the floor, as the case 



PLANS FOR PIPE SYSTEMS 



107 




a=[F==^^===^ 



Dnm-c// 



«I3 



"2=13 



Fig. 103. — The circuit system of hot-water heating. 




Fig. 104. — Part of plan of drainage system in building. 



108 



ADVANCED SHOP DRAWING 



may be. The size of the riser is shown between the various 
floors, by heavier type. 

Piping plans are often shown as isometric drawings. Figure 
102 shows an isometric drawing of a corner pipe coil. Such a 



I? 



5 

Q 
I 



W.P. 




/ 
/ 
/ 
/ 

\ 

/ 



S,V/P. = sink Wa^ie Pipe 
PT. = Oiscont^ecfiMQ Trap 



s. ., 

/ 

\ 

R.W.P. 

t in 30 




fNDEX 

S.P.^ Soil Pipe 
W.P.= Waste Pipe 
Cl.T = alley Trap 
P.W.P. = Path Wafer Pipe 

V.R = Vehiilatmij Pipe 



'V 



\zzz:^^ 



C 
if 

o 



f::::^ 



OX NOjZ. 



D.TNO.i. 



Fig. 105. — Drainage plan of a detached house. 



coil might be used as a radiator in a gymnasium or bathing pool 
where the good appearance of the radiator is not necessary. Fig- 
ure 103 is an isometric drawing of a hot-water heating system for 
the first floor of a building. This is a one-pipe system. 



PLANS FOR PIPE SYSTEMS 



109 



and V\e/^/7fs 



Fof Equal ix.inq Pipe ■ 

To Darnp 
iReguiaf 




^Ma'in Return, 



\ [,[ Fig. 106. — Typical boiler connections. 



W///////////////.^ 




^ Em. Si. for 






^ 




Fig. 107. — Pipe plan for power house. 



no 



ADVANCED SHOP DRAWING 



A part of the plans of the drainage -system of a building is 
shown in Fig. 104. Cast-iron piping is commonly used in such 
systems. 

Underground pipe lines are usually line drawings, accompanied 
by a key. Figure 105 shows the plan for the drainage system of a 
detached house. The pipe sizes together with their gradients 
are shown. 

Pipe drawings for power plants are generally more complicated 
than those for dwellings, because of the greater number and 




£/ev<7^/or7. 

Fig. 108. — Plan for boiler feed piping. 

variety of fittings used. It is in this branch of drafting that one 
may expect the more common use of the diagrammatic drawings 
and line symbols. 

Figure 106 shows typical connections between two boilers. 
Figure 107 shows a plan and elevation drawing for the piping for 
a power house. The steam passes directly from the boilers to 
the steam drum or ''header" from which it passes to the various 
engine cylinders through individual pipes. Figure 108 is an 
example of feed piping and illustrates the use of crosses in the 
mains to designate the various pipe fittings. Appropriate notes 
are always placed at such points. 



PLANS FOR PIPE SYSTEMS 



111 







B Of/ens ^ 



ao 



QlQ 



f'eei/ kafer Main-^ 
Feed Water Httai^r 

i^Oil 3ef>anator ^Exhaust P,p>es 



Injector 



4 



V~\£ngine M I 
\ \Cyf1nder3 J 



FeedWdkr 
Supply 



-* — mfk 



Fig. 109. — Exhaust and feed piping for non-condensing plant. 



(A 



Q-Q 



•iG/ohe >taNe 



Gj3 






/njecTor Main 



^ Bo/'/ers 



All hiofi pressure drips, returns 
nea\ 




^fnjector 



^^ . By- Pass 

■from heating system. e/K:., enter "^ 

opan heater ^-^^Open tfeater 



f<^ 

r .i.T — t — jF^ 



<y 



Co Id W<fter3uf>ffly 






Fig. 110. — Feed piping with open heater. 



112 



ADVANCED SHOP DRAWING 



Line diagrams are quite often used in laying out pipe systems 
for industrial plants. They are commonly used for making the 
prehminary sketches. Figure 109 and Fig. 110 are typical 
examples of diagrammatic pipe drawings though the sizes of the 
pipes are not shown. In both of these figures the boilers are 



Pipe 



Table of Pipe Symbol-S. 

o II 

Riser Union 



Elbow 



Tbe 



Cross 



^S Elbow 



T 

Coc^ 



-5- 



Any TrnoF Yalve Globb Ya,lv£ 



-<>- 



Ch£ck Valve 



GAre Valvs 



Injector En(^ine Cylinder 



Pump 



Air Pump 



Receivbr 



£CCNCM/Z£R 



o 

'METE.R 




o 

Hot Well. 



O 



H£ATE.R - COA/OMHSER 



Boiler 

Table 7. 



CUD 



Battery or Boil.ers. 



shown in elevation, while the rest of the drawings are plan 
views. 

Table 7 is a table of line symbols which are used by recognized 
authorities. These are recommended to the consideration of the 
reader. If a fitting is used, for which no symbol is shown in this 



PLANS FOR PIPE SYSTEMS 



113 



table, it may be represented in some such simple manner as will 
represent its outline, generally by means of a rectangle or circle 
with a name to indicate the fitting. 






7 



y 



Check li'a/fe 
Gtoie yafye 









/fijecfor 



^'v. 



J^ 



tly-Paii 



,G. V. 



2/^i/)i.ili'ary 
\ Heafer 
6y. 



Valves _<»-^ -^ ^ ^ 



d5.v. 



(3.V. 



Z 



^ 



Val\re 



Y^ ^ot^e// 



'.->»J G.V. 






By Fa Si 



Hefizr 



Hfoter 



/Vote 



{ 



Q.V~G/o6e Valve. 
CM- Check Va/vc 



O Surface 



Condenser 



\ \ Air Pt/mp 

C Surface 
Cont/pni 



G.V, 



Condenz^r 



]{ Air fump 

r~) ■Svrfacv 
Condenser 



Fig. 111. — Feed piping for condensing plant. 



Problem 18 

Figure 111 shows a pipe diagram of the feed piping for a condensing 
plant. The fittings are noted at their respective places but are not shown. 
The lines are to be laid out on a standard sheet of drawing paper. The 
drawing should be made as large as convenient, but the lines should be 
placed in somewhat the same relative position that they occupy in Fig. 111. 
The symbols for the fittings are to be added, and the drawing is to be 
finished after the method shown in Fig. 109 and Fig. 110. The symbols 
for the various fittings may be obtained from Table 7. 



CHAPTER IX 



SHEET-METAL WORK 



57. Fundamental Principles. — Sheet-metal drafting deals pri- 
marily with the intersections and developments of surfaces. It 
is, therefore, necessary that the fundamental principles should 
be mastered in the abstract examples which follow. The appli- 
cations of these principles to practical problems are numerous, 
and a few of them will be mentioned. A few fundamental prin- 
ciples will first be explained without applying them to any 
particular problems. 




Fig. 112. — Development of cylinder intersected by plane. 

The case of a plane intersecting a cylinder, as in Fig. 112, will 
first be considered. This might be a case of a ventilator or a 
chimney passing through a sloping roof. The plan and elevation 
views are show^n to the left. The intersecting plane is perpen- 
dicular to the plane of the paper and is represented by the line 
AB. 

114 



SHEET-METAL WORK 115 

If it is desired to see the intersection of the plane and cyhnder 
in true size, it must be viewed along a line perpendicular to 
AB. Therefore, its projection upward may be drawn on lines 
perpendicular to AB. Its long dimension Cs-is will evidently be 
the length 1-7, while its width /3-I3 will equal fi-l, of the upper 
plan view. To obtain the width of the true section at any other 
point as es-M^, projection lines parallel to/s-ls, as ms-S, to meet^B 
in 3 should be drawn; 3 should be projected to the upper plan thus 
obtaining width €i-nii equal to es-nis in the true section. Widths 
at any other points may be similarly found. It will be noticed 
that the true section formed by the intersection of a cylinder and 
a plane is an ellipse. If the case was that of a ventilator passing 
through a roof, the use of this intersection could be seen in laying 
out the hole to be cut in the roof. 

58. Developments. — If it is desired to make this cylinder or 
one of the parts of it out of sheet metal, it will be necessary to 
lay it out or develop it on a flat surface. The procedure of 
development is as follows: 

The base line of the development should be projected over to 
the right from the elevation. The length of this base line, C2-C2, 
should be equal in length to the circumference of the cylinder, 
which equals 3.1416 times the diameter. The height of the develop- 
ment may be projected over from the elevation. The develop- 
ment of the complete cylinder is C2-P-0-C2. 

If it is desired to develop that part of the cylinder beneath 
the plane AB, the circle of the plan view should be divided 
into a number of equal parts. The base line, C2-C2, should be 
divided into the same number of equal parts and perpendiculars 
erected to it at each of the points of division. The points should 
be projected from the plan view upon the elevation. Such imagi- 
nary lines as appear on the surface of the elevation are known as ele- 
ments. They intersect the plane AB in points 1, 2, 3, etc. 
These points should be projected over to their positions on their 
respective elements in the development as shown. A smooth 
curve passed through these points will define the upper edge of 
the development. The development for that part of the cylinder 
below the plane AB is C2-l'-7'-l'-^2. 

59. Curves and Circles. — ^For drawing curves such as l'-7'-l' 
in Fig. 112 the draftsman uses irregular curves. These are made 
of the same material as triangles but have edges of various irreg- 
ular outlines. The draftsman uses that part of the outline 



116 



ADVANCED SHOP DRAWING 



which approximates most closely the curve which he wishes to 
draw. 

For dividing circles into a number of equal parts, a protractor 
is often used. A protractor is usually made of amber or brass. 
It is semi-circular in form, and has its circular edge graduated 
in degrees. 

60. Intersections. — Figure 113 shows the construction for a 
right cone intersected by a plane. Aright cone is one whose base 




Fig. 113. — Construction and development of right cone intersected by pi 



ane. 



is perpendicular to its axis. The apex of the cone is Wi; the base 
is ai-Qi. The intersecting plane lies at an angle with the horizon- 
tal, but in the elevation of the cone it is perpendicular to the 
plane of the paper. The^^Dlane, therefore, appears as a straight 
line l'-7' in the elevation. To find the intersection in the plan 
view the following procedure is suggested. 



SHEET-METAL WORK 117 

In the plan view, the circular base a-g should be divided into 
a number of equal parts. From each of the points of division, 
lines should be drawn to the vertex m as shown. The points 
a, h, c, etc. should be projected down on the base hne a^-gi in 
the elevation. These points should be connected with the vertex 
mi. These lines in elevation will be the projections in the 
elevation of the corresponding lines just drawn in the upper plan. 
They represent elements on the surface of the cone. In eleva- 
tion, these elements intersect the cutting plane in the points V , 
2' , 3', etc. These points should be projected up to their respec- 
tive elements in the upper plan as shown. A curve passed 
through the points thus determined outlines the intersection in 
the plan view. The section cut by the passage of this plane may 
be seen in the shaded view to the right. It is obtained in the 
same manner as was the true section in Fig. 112. 

The development of the cone is obtained by striking the sector 
of a circle mi-g^-g^ with a radius equal to nii-ai and with the 
computed circumference of the base pointed off as ^2-6^2- 

If this cone were cut by an inclined plane V-1' , the lower part 
of the cone, V-l'-gi-ai, would form what is known as the frustum 
of a cone. The development of this frustum is made as follows : 

The position of the various elements which have been deter- 
mined in the plan and elevation should be shown on the 
development. In the elevation, the elements rui-ai and mi-gi 
lying in the plane of the paper are the only elements which appear 
in true size. All the other elements do not appear in true size 
because they represent lines which are inclined to the surface 
of the paper. The several points in which these line elements 
intersect the cutting plane must, therefore, be projected over to 
the position of the line mi-ai by projection lines parallel to the 
base of the cone. From their projections on mi-ai and with m^ 
as center, the projections of V , 2', 3', etc. may be swung around 
on to their respective elements in the development as shown. A 
smooth curve 1"-l"-7'' passed through these points determines 
the line of intersection on the development. The development 
of the frustum of the cone is 1"-l"-l"-g2-g2. A piece of sheet 
metal cut out hke this development could be rolled up so as to 
form the frustum of the cone. It should be noticed in this devel- 
opment and future ones how the sheet-metal w^orker generally 
plots the developments so that the seam will come on the short 
edge. 



118 



ADVANCED SHOP DRAWING 



The aim should be to master all the elementary principles in- 
volved in these abstract problems. To follow the foregoing 
rules blindly will not aid in solving new problems as they arise. 

61. Materials Used. — In applying these principles to actual 
problems in sheet-metal work, it would be well first to know 
something of the metals used, how they are sold, worked, etc. 

Sheet metals are made in various gages or thicknesses and may 
be designated by the gage numbers or by the actual thicknesses. 
There is a wide difference between the various gage systems now 
in use. For this reason it is always best to specify the thickness 
of the metal either in decimal or fractional parts of an inch. 

Table 8 shows the U. S. Standard Table for sheet and plate 
iron and steel adopted by Congress in 1893 for the sake of uni- 
formity, and is the table by which government duties and taxes 
are levied on these articles. For gages number 20 or thinner, it is 
assumed in the development of the pattern that one is dealing 
with no thickness, and no allowance is made for bending or rolling 
in the machine. But where the metal is of heavier gage than 
number 20, allowances must be made for the thickness of the 
metal. 



Table 8. — U. S. Standard Gage for Sheet and Plate Iron and 

Steel, 1893 



Number 
of gage 


Approximate thick- 
ness in fractions 
of an inch 


Approximate thick- 
ness in decimal 
parts of an inch 


Weight per 

square foot 

in ounces 


Weight per 
square foot 
in pounds 


0000000 


1-2 


0.5 


320 


20.0 


000000 


15-32 


0.4688 


300 


18.75 


00000 


7-16 


0.4375 


280 


17.50 


0000 


13-32 


0.4063 


260 


16.25 


000 


3-8 


0.375 


240 


15.0 


00 


11-32 


0.3438 


220 


13.75 





5-16 


0.3125 


200 


12.50 


1 


9-32 


0.2813 


180 


11.25 


2 


17-64 


0.2656 


170 


10.625 


3 


1-4 


0.25 


160 


10.0 


4 


15-64 


0.2344 


150 


9.375 


5 


7-32 


0.2188 


140 


8.75 


6 


13-64 


0.2031 


130 


8.125 


7 


3-16 


0.1875 


120 


7.5 


8 


11-64 


0.1719 


110 


6.875 



SHEET-METAL WORK 



119 



Table 8. — Continued. 



Number 
of gage 


Approximate thick- 
ness in fractions 
of an inch. 


Approximate thick- 
ness in decimal parts 
of an inch 


Weight per 

square foot 

in ounces 


Weight per 
square foot 
in pounds 




9 


5-32 


0.1563 


100 


6.25 




10 


9-64 


0.1406 


90 


5.625 




11 


1-8 


0.125 


80 


5.0 




12 


7-64 


0.1094 


70 


4.375 




13 


3-32 


0.0938 


60 


3.75 




14 


5-64 


0.0781 


50 


3.125 




15 


9-128 


0.0703 


45 


2.813 




16 


1-16 


0.0625 


40 


2.5 




17 


9-160 


0.0563 


36 


2.25 




18 


1-20 


0.05 


32 


2.0 


• 


19 


7-160 


0.0438 


28 


1.75 




20 


3-80 


. 0375 


24 


1.50 




21 


11-320 


0.0344 


22 


1.375 




22 


1-32 


0.0313 


20 


.1.25 




23 


9-320 


0.0281 


18 


1.125 




24 


1-40 


0.025 


16 


1.0 




25 


7-320 


0.0219 


14 


0.875 




26 


3-160 


0.0188 


12 


0.75 




.27 


11-640 


0.0172 


11 


0.688 




28 


1-64 


0.0156 


10 


0.625 




29 


9-640 


0.0141 


9 


0.563 




30 


1-80 


0.0125 


8 


0.5 




31 


7-640 


0.0109 


7 


0.438 




32 


13-1280 


0.0102 


6>^ 


0.406 




33 


3-320 


0.0094 


6 


0.375 




34 


11-1280 


0.0086 


5^^ 


0.344 




35 


5-640 


0.0078 


5 


0.313 




36 


9-1280 


0.007 


^yi 


0.281 




37 


17-2560 


. 0066 


m 


0.266 




38 


1-160 


0.0063 


4 


0.25 



Table 9 is the table for sheet copper which was adopted as 
standard by the Association of Copper Manufacturers of the 
United States. For convenience, the nearest Stubbs' gage 
number is shown for the various thicknesses of copper but it is 
preferable to use the decimal thicknesses. The various com- 
mercial sizes of sheets and their weights are also shown. 



120 



ADVANCED SHOP DRAWING 



Tablf 9. — Adopted by the Association of Copper Mfrs. of the U. S. 


Stubbs' 

gage 
(nearest 
number) 


Thickness 

1 in decimal 

parts of 

an inch 


Ounces 

per 
sq. ft. 


Sheets 
14X48 in., 

weight 
in pounds 


Sheets 
24X48 in., 

weight 
in pounds 


Sheets 
30X60 in., 

weight 
in pounds 


Sheets 
36X72 in., 

weight 
in pounds 


Sheets 
48X72 in., 

weight 
in pounds 


35 


0.00537 


4 


1.16 


2 


3.12 


4.50 


6 


33 


0.00806 


6 


1.75 


3 


4.68 


6.75 


9 


31 


0.0107 


8 


2.33 


4 


6.25 


9.00 


12 


29 


0.0134 


10 


2.91 


5 


7.81 


11.25 


15 


27 


0.0161 


12 


3.50 


6 


9.37 


13.50 


18 


26 


0.0188 


14 


4.08 


7 


10.93 


15.75 


21 


24 


0.0215 


16 


4.66 


8 


12.50 


18.00 


24 


23 


. 0242 


18 


5.25 


9 


14.06 


20.25 


27 


22 


0.0269 


20 


5.83 


10 


15.62 


22.50 


30 


21 


0.0322 


24 


7.00 


12 


18.75 


27.00 


36 


19 


0.0430 


32 


9.33 


16 


25.00 


36.00 


48 • 


18 


0.0538 


40 


11.66 


20 


31.25 


45.00 


60 


16 


0.0645 


48 


14.00 


24 


37.50 


54.00 


72 


15 


0.0754 


56 


16.33 


28 


43.75 


63.00 


84 


14 


0.0860 


64 


18.66 


32 


50.00 


72.00 


96 


13 


0.095 


70 




35 


55.00 


79.00 


105 


12 


0.109 


81 




40K 


63.00 


91.00 


122 


11 


0.120 


89 




44K 


70.00 


100.00 


134 


10 


0.134 


100 




50 


78.00 


112.00 


150 


9 


0.148 


110 




55 


86.00 


124.00 


165 


8 


0.165 


123 




61 


96.00 


138.00 


184 


7 


0.180 


134 




67 


105.00 


151.00 


201 


6 


0.203 


151 




753-^ 


118.00 


170.00 


227 


5 


0.220 


164 




82 


128.00 


184.00 


246 


4 


0.238 


177 




88K 


138.00 


199.00 


266 


3 


0.259 


193 




96 


151.00 


217.00 


289 


2 


0.284 


211 




105^^ 


165.00 


238.00 


317 


1 


0.300 


223 




niy2 


174.00 


251.00 


335 





0.340 


253 




126M 


198.00 


285.00 


380 







Fig. 114.— Method of 
wiring edge. 



In dealing with tin plate, no considera- 
tion is given to thickness and, consequently, 
no allowance is made when rolling or bend- 
ing it in the machine. 

For wiring, that is, wrapping the metal 
around a wire along the edges for the sake 
of stiffness, an edge J^" wide is provided 




SHEET-METAL WORK 121 

outside of the pattern. Figure 114 shows such an edge bent 
ready for wrapping at A, and wrapped at B. 

62. Seams. — Figure 115 shows the lock seam such as is com- 
monly used for vertical seams. In this type of joint, allowance 
must be made for three times as much material as in the case of 
wiring, because the joint has three laps. Metal for one of the 
laps is provided on one edge of the pattern, while provision for 
the other two laps is made on the mating edge of the pattern. 

Figure 116 shows the two operations in making a joint that is 
used in fastening the bottom to the 
body of a vessel. 

The notching of patterns is an 
important detail. Notches are 
shown on those edges which are 



Fig. 116. — Lock seam for 
Fig. 115. — Lock seam for fastening the bottom to the 

vertical seams. body of a vessel. 

provided for seaming and wiring, and it is essential that they 
should be accurate so as to produce a finished job. 

When the patterns have been cut in paper, they are then placed 
on the sheet metal and a few weights laid on top of the paper to 
hold it down. Slight marks are then made through it with a 
sharp scratch awl or prick-punch, larger dots indicating a bend. 
The paper is then removed and lines scribed on the plate, using 
the scratch awl for making the straight lines and a lead pencil 
for making the curved lines. Laps are then added as required 
after which the shape is cut out of the metal. 

Figure 117 shows a typical sheet-metal design in which a half 
pattern has been developed for a bucket. Part patterns like 
this are often necessary, owing to the fact that sheet metal is sold 
in commercial sizes. The designer and workman should always 
aim to use material as economically as possible. It should be 
noted how provision has been made for wiring the upper edge; 
also how twice as much material has been provided on one edge 
as on the other on account of the lock seams. 

Figure 118 shows a ventilator with a hood and a deflector above 
and with a flare below. This is a problem in cone development 
entirely and is submitted as a sample problem for individual study. 
A detail of the joint between the hood and deflector will be 



122 



ADVANCED SHOP DRAWING 




Fig. 117. — Half pattern development of bucket. 





Fig. 118. — Ventilator with hood and deflector. 



SHEET-METAL WORK 



123 



found in the development of the hood. It will be noticed that 
provision has been made for a lock seam on the outer edge of 
the development of half of the pattern for the hood and the 
deflector. The outer diameters of the conical parts are usually 
made twice that of the pipe. The dimensions are omitted for 
the sake of clearness. 

Thus far only curved surfaces intersected by planes have been 
dealt with. The intersections and developments of bodies whose 
surfaces consist of many planes will now be considered. 

63. Prism Intersection. — Figure 119 shows an octagonal prism 
intersected by a plane. This construction is a great deal like 
that for Fig. 112 except that it is not necessary to assume any 



f/O^ 



v^-k 




Fig. 119. — Octagonal prism intersected by plane. 

elements on the surface of the prism ; it is necessary to deal only 
with the corner elements a, b, c, etc. in the upper plan view. 
One of the fundamental principles of sheet-metal drafting is 
that two planes always intersect in a straight line. In this case, 
then, it is necessary merely to determine the intersection of the 
plane MN with the eight plane faces of the prism. 

The right side view of the prism might have been drawn by 
transferring the dimensions of width from the upper plan by means 
of the dividers. A simpler plan still, and one that is universally 
used in sheet-metal work, is to project the various dimensions of 



124 



ADVANCED SHOP DRAWING 



height in the upper plan over to a vertical line o-p, as shown in 
Fig. 119, then from some center on this line as r, revolve these 
several points of projection into the horizontal. This will 
determine the several points of projection on r-s as shown. By 
this means all dimensions of height in the upper plan may be 
readily revolved to determine the dimensions of width in the 
side view. It will be seen that p-h in the upper plan equals ai-bi 
in the right side view and that all other dimensions of height in 
the upper plan equal those of corresponding width in the right 
side view. The method by which the intersection is determined 
in the right side view should be given special attention. The 
true section appears to the left. In all of these cases it will be 
noticed that it is necessary only to determine the points in which 
the corner elements of the prism pierce the plane M-N and then 
to connect these consecutive points by a series of straight lines. 

64. Prism Developments. — The development of the lower 
part of the prism of Fig. 119 is shown in Fig. 120. It will be 





> 


y^ 


ii 


N 




/ 


1 ■' 
1 






\ 


K, 




/^ 




1 


V 






T 
1 














-< 


k *] 


^- ->-■« 




f- ->- 


k ■*{ 


k ^ 


^- 





Fig. 120. — Development of lower part of prism of Fig. 119. 

noticed that the edge produced by the intersecting plane M-N 
is made up of straight lines. The system of dimensioning such 
developments is also indicated. The outside elements of pat- 
terns which close like this are always of equal height. It should 
be noticed again how developments are generally laid out so 
that the seam comes on the short edge. 

The intersections and developments of a pyramid follow the 
same general principles as are applied to a cone. Figure 121 
shows the elevation and plan views of a square pyramid. The 
line mi-hi in the elevation represents the surface m-b-c in the plan 
view and is, therefore, not the true length of one of the corner 
elements, such as m-b, with which radius the development must 



SHEET-METAL WORK 



125 



be struck. The true length of the Hne 7n-x is represented by 
mi-bi, but the true length of m-h is desired. To obtain the true 
length of the corner element m-6 the following method may be 
used. 

The horizontal center line should be drawn in the plan view; 
also ai-bi should be extended in a horizontal direction toward 
the right. With m as a center and a radius m-b, an arc should be 




n. b, °Jt 

Fig. 121. — Development of square pyramid intersected by plane. 



described which will intersect the horizontal center line of the 
plan view in the point y. The point y should be projected upon 
the extension of ai-bi giving the point a2. Then mi-a2 will be 
the true length of the corner element m-b or any other corner 
element. With m as a center and mi-a2 as a radius the arc of the 
development a2-C2-«2 should be struck and the corner elements 
drawn. 

If the pyramid be intersected by a plane ei-/i, the various 
points where the plane intersects the corner edges in the eleva- 



126 ADVANCED SHOP DRAWING 

tion must be projected over to mi-a2 by horizontal lines, thus 
locating the intersection on the true length of the corner elements. 
These points should then be projected upon their respective ele- 
ments in the development by means of arcs struck from rui as 
center. The intersection will then follow the lines e2-f2-g2-h2-e2 
on the development, and will consist of a series of straight lines, 
because the plane ei-fi intersects the plane surfaces of the 
pyramid in straight lines. 

The true section appears to the left on projection lines per- 
pendicular to ei-fi. 

The problem shown in Fig. 121 involves principles which are 
commonly encountered in intersecting bodies which have plane 
surfaces. These problems are quite usual in ventilating and 
hot air heating systems. 

In Fig. 122 a square prism is shown standing on end, inter- 
sected on the right by a square prism, two of whose faces are hori- 
zontal. In determining the intersections of these two bodies 
one may proceed as follows: 

The upper plan and elevation views of the vertical prism should 
be drawn and then its right side view drawn by the method which 
was shown in Fig. 119. Next the end view of the horizontal 
prism should be drawn in the right side view as shown. The 
end views of figures should always be drawn first. Then the 
horizontal prism in the upper plan view should be drawn by the 
method of Fig. 119. From the points in which its corner ele- 
ments intersect the side faces of the vertical prism in the upper 
plan, vertical projection lines should be drawn downward to 
intersect horizontal projection lines drawn from the right end 
view. Connecting this series of intersecting points by a series 
of straight lines will determine the intersection in the elevation. 
The development for either prism may be readily plotted since 
all the elements of both prisms are parallel to the plane of the 
paper in the elevation. 

The left half of Fig. 122 represents the same vertical prism 
intersected on the left by a square prism, as before, with the 
exception__^that^in^this case two of its faces make angles of 30° 
with the horizontal. The drawing is fully marked so that the 
construction^may be readily followed. The intersection in the 
front elevation can be determined readily by projecting from the 
left and upper plan view, the various points being determined in 
the consecutive order in which they appear in the left end view 



SHEET-METAL WORK 



127 



along the lines i-j-k-l. Particular notice should be taken how 
the surfaces i-j and k-l each intersect the two faces a — h and a — d 
of the vertical prism, and how this affects the intersection in the 
front elevation. It will be noticed, as before, that the intersection 
consists of a series of straight lines, because it is determined by 
the intersections of a series of plane surfaces. 

It would be well to consider now the intersection and develop- 
ment of two bodies having curved surfaces; for instance, two 
cylinders. This problem is illustrated in a steam dome on a 
boiler, in tapping into pipe lines, in hot air heating pipes which 
are circular and intersect, and in numerous other cases. 




ni6Hr END 
VIEW 



ELEVATION 

Fig. 122. — Intersections of three square prisms. 



In determining the intersection of two cylinders, one may pro- 
ceed in the same order as in the previous examples, drawing the 
end views of each cylinder first as in Fig. 123. When the cyl- 
inders have been shown in the upper plan, front elevation, and 
right end views, it remains to determine their intersection in the 
front elevation. This may be done as follows: 

The circumference of the small cylinder in the upper plan view 
should be divided into a number of equal parts. These will 
determine the elements on its surface which are equally spaced, 
as 1, 2, 3, etc. They intersect corresponding horizontal ele- 
ments shown on the surface of the large cylinder in the same view. 
The positions of these several elements on the large cylinder may 



128 



ADVANCED SHOP DRAWING 



now be determined in the right end view by the method of pro- 
jection shown in the figm-e. By means of vertical projection Hnes 
drawn downward from the upper plan, and intersecting horizon- 
tal ones drawn from the right end view, a series of points which 



UPPER 
PLAN 



\ \ \\ \ 

.N\\\\V> 




Fig. 123. — Intersections of cylinders. 



' 




r^ 


■ 


• 




■ 


■— 


p-1 


■ 


' 


r-n 


■ ' 




, ' 


' 








■» ■* 


V 4.J 


I J 




> « 


• « 




* -• 


«■ ■» 


» » 


« • 







T 
1 



Fig. 124. — Development of small cylinder of Fig. 123. 

define the intersection in the elevation may be determined. 
Since both intersecting surfaces are curved, their intersection 
in the elevation will also be a curved line. A smooth curve 
should, therefore, be passed through the series of points just 
determined in the front elevation. 



SHEET-METAL WORK 



129 



The development for the small cylinder of Fig. 123 together 
with appropriate dimension lines is shown in Fig. 124. 

Problem 19 

Develop patterns for the various parts of the hand scoop shown in Fig. 
125. Also show a drawing of the scoop as shown in this figure. All these 
views should be arranged upon one sheet and should be drawn to appropriate 




Hand Scoop 

3heef Copper -.0269''fhick 

Fig. 125. 

scales. Dimension all developments completely. In scaling the develop- 
ments to dimension them, be sure to use the same scale to which the devel- 
opments have been drawn so as to obtain the full size dimensions of the 
scoop. 

In the side view it will be seen that the center line of the handle is inclined 
30° to the horizontal and that it meets the back of the scoop on the hori- 




FiG. 126. 

zontal center line of the body. A flaring boss serves to strengthen the handle 
where it meets the back. It will be noticed by the construction lines which 
have been supplied that this boss is a part of a right cone. The intersection 
of the boss and handle is at right angles to the center line of the handle. 

The body of the scoop should be developed first and provisions made for 
a lock seam on the upper surface. This can be developed according to the 
9 



130 



ADVANCED SHOP DRAWING 



principles indicated in Fig. 112. First lay off a base line of appropriate length. 
Divide the left end view into a number of equal divisions. Project these 
over to the side view and thus determine the lengths of the several elements 
which should be erected on the base line. Pass a smooth curve through 
their ends. After the pattern has been thus determined, it may then be 
dimensioned at various points as shown in Fig. " 126. It is not necessary 
that the dimensions given should be those of the identical elements by 
which the outline of the pattern was obtained. 

When the circular pattern has been developed for the back, an edge must 
be provided outside of the pattern and properly notched, as shown in Fig. 
127, so that it may be soldered onto the body. 




Fig. 127. 



The boss should have a lock seam along its top and a notched edge for 
soldering it to the back. The junction of the boss and handle is at right 
angles to the center line of the handle and may be considered as a plane 
intersecting a right cone on the left, and a plane intersecting a cylinder on 
the right. 

The cylindrical handle should have a lock seam along its length and have 
a notched edge for soldering into the boss. 

A circular piece properly notched is to be soldered into the outer end of 
the handle. 

Problem 20 

Figure 128 shows a right pyramid with a base 3 ft. in. X 4 ft. in. and 
altitude 3 ft. in. intersected by a cylinder 2 ft. in., the center lines of 
both being coincident. Such an arrangement as this might serve for a 
smoke connection for a boiler; if inverted, it might serve as a hopper for a 
bin. 

Determine the intersections and developments of the two parts. In 
determining the development of the pyramid, it will be necessary to deter- 



SHEET-METAL WORK 



131 



mine the true length of each element as was explained in Fig. 121. Develop 
a full pattern for the cylindrical part and make provision for a lock seam. 
Show a half pattern for the pyramidal part with lock seams running up the 
center of the sides which are 3 ft. in. long. Also provide the pyramid with 
an edge for a seam where it connects to the cylindrical part. 




Fig. 128. 



CHAPTER X 
SHEET-METAL WORK (Continued) 

65. Triangulation. — Thus far, only those surfaces have been con- 
sidered which have parallel-hne elements on their surfaces, as 
in the case of the cylinder and the prism, or radial-line elements, 
as in the case of the cone and the pyramid. Patterns are often re- 
quired which cannot be determined by either of these two meth- 
ods. Hence, in the development of any irregular article, it 
is necessary to measure up the surface part by part, and 
then add one to another until the entire surface is developed. 
This is known as development by triangulation, and depends for 
its results on two general principles : first, to find the true lengths 
of all lines, real or assumed, appearing on the surfaces of the solid; 
second, having determined the true lengths of such lines, to con- 
struct triangles similar in form and relation to those shown on 
the solid. 

66. Development by Triangulation. — ^In the case of the pyra- 
mid, Fig. 121, it w^as necessary to determine the true length of one 
of the corner elements before the development could be drawn. 
A method for doing this was shown. It would be well to con- 
sider a few facts in connection with Fig. 121. The true length 
of a corner element was found to be m,ia2. This is the hypot- 
enuse of the right triangle, 7ninia2. It will be seen that nia2 = 
my = mh, which is the horizontal projection of this corner ele- 
ment in the upper plan. The vertical height of mi6i is mini, 
which is the projection of the corner element in the front eleva- 
tion. Hence, the general truth: 

The true length of a line is equal to the hypotenuse of a right 
triangle, one of whose legs is equal to the foreshortened line in the 
plan view, while the other leg is equal to the vertical height of the 
same line in the elevation. 

To illustrate the use of this principle, suppose it is desired 
to determine the true length of any other line in the frustum of 
this pyramid, as the line a-e, shown in the plan view. Let 
Fig. 129- A be a copy of the frustum of the pyramid shown in 

132 



SHEET-METAL WORK 



133 



Fig. 121. Then in Fig. 129-A to find the true length of the 
Hne a-e according to the rule just given, a vertical line should be 
j&rst passed through ei to meet the base in a point ii. The line 
ii-ei will then be the vertical height of the element ai-ei 
in the elevation. To the right in Fig. 129-B a right triangle 




a, L 




^2 



• '' (B) ' 



Fig. 129. — Development by triangulation. 

should be constructed in which one of the legs 12-62 equals 
ii-ei and the other leg 22-^2 equals ae in the upper plan. 
The hypotenuse of this triangle, 02-^2, is the true length of 
the corner element a-e. By the construction of similar right 
triangles, with the aid of construction lines to determine the 



134 ADVANCED SHOP DRAWING 

vertical heights in the front elevation, the true lengths of the 
lines h-f and e-f as shown may be determined. The line d-h 
equals a-e; h-g equals e-f; and c-g equals h-f. The lines a-b, h-c, 
c-d, d-a, h-e, smdf-g are shown in true length in the plan view. 

To develop the side faces of this frustum by triangulation, 
it will be necessary first to divide the various surfaces up into 
triangular areas as shown by the broken lines in the upper plan. 
The true lengths of each of these lines is determined as in the 
previous cases. 

First a line should be drawn equal to the length of one edge, 
as as-es, Fig. 129-C, which is equal to 02-^2 as in Fig. 129-5. 
With radius 62-62 and ez as a center, an arc should be described. 
With radius a-h and a^ as a center, another arc should be de- 
scribed to intersect the first arc in point 63. Upon the line 63-63 
the triangles 63-63-/3 may now be constructed in a similar manner, 
locating point /s with two intersecting arcs, one drawn with a 
radius 62-/2- This method may be continued to determine the 
entire development. This development by triangulation may 
be superimposed upon that obtained in Fig. 121 by the radial 
line method. The two will be found to coincide. 

This method of solving problems by triangulation is equally 
applicable to curved surfaces such as the flashing around chim- 
neys, gusset plates on locomotives, flaring ends of bathtubs, 
coalhods, foot-bath pans, etc. The case of the irregular solid 
shown in Fig. 130- A will now be considered. Its two bases are 
parallel. The upper base is circular, and the lower one is oval. 
In solving this problem by triangulation, the draftsman must first 
conceive that the upper and lower bases are joined by a series of 
triangular surfaces as suggested by the series of straight light 
lines connecting both bases. Seeing the construction and solu- 
tion of problems in the mind's eye like this is a valuable aid in 
the solution of sheet-metal problems. It will be seen that the 
object is symmetrical on both sides of the horizontal center line 
passing through the upper plan. If a development is made of 
the lower half of one figure, a duplication of it will give the com- 
plete development. 

In drawing the imaginary triangles, the outlines of both bases 
in the upper plan should be divided into the same number of 
equal parts, and the alternate points of division on each connected 
by a series of straight lines as shown. These points and their 
lines should then be projected down to the front elevation. It 



SHEET-METAL WORK 



135 



will be seen that the lines a-h and n-o appear in true length 
in the elevation. The true lengths of the other hnes must now be 
determined. This is best done by extending indefinitely toward 
the right the two lines which represent the bases in the elevation. 
Beginning at some point in this line as hi, hi-Ci should be 
pointed off equal to b-c in the upper plan, and Ci-di equal 
to c-d, etc. Since the vertical heights of all these lines in the 
elevation are equal, and are equal to the distance between the 
two parallel lines just extended to the right, perpendiculars may 
next be erected at each of the points just pointed off on the ex- 
tended base line. From the points where these perpendiculars 




Fig. 130. — Development of irregular solid by triangulation. 



intersect the upper base line extended, straight lines may be 
drawn to connect the alternate points on the lower base line ex- 
tended. These lines will represent the true lengths of the several 
lines forming the triangles. For instance, the diagonal line 
between bi-Ci equals the true length of h-c; the diagonal be- 
tween Ci-di equals the true length of c-d, etc. 

The true lengths of all the lines having now been determined, 
the development may be constructed. Fig. 130-C The line 
a2-b2 should be drawn equal in length to a-b in the front 
elevation. With ^2 as a center and a radius equal to a-c in the 
plan, an arc should be described. With 62 as a center and a radius 
equal to the diagonal between bi-Ci, an arc should be described 
to intersect the one just drawn in point C2. Similar constructions 
should be continued for the rest of the triangles. Smooth 



136 



ADVANCED SHOP DRAWING 



curves passed through the upper and lower rows of points thus 
determined will give a development of the half pattern desired. 

The principles shown in these few simple illustrations are 
applicable to the solution of any problem by triangulation. 

67. Elbows. — No other article is so common to the sheet- 
metal worker's trade as the pipe elbow. The general method to 
be pursued when a development is required for a two-piece 
elbow forming an angle of 90° is the same as that for two inter- 
secting cylinders, or for a cylinder intersected by a plane at an 
angle of 45° to the axis. There is, however, a more simple 
method by means of which a pattern may be developed for an 





Fig. 131. — Pipe elbows. 

elbow of any number of pieces or for any given angle. The drafts- 
man should become familiar with this construction because it is 
very commonly used in the sheet-metal trade. 

Suppose it is desired to develop patterns for elbows of any 
number of pieces. The three elbows show in Fig. 131 are typical 
examples and will be referred to by way of illustration. The 
elbows shown at A and B in Fig. 131 are known as square elbows, 
because if lines be drawn perpendicular to the center lines of the 
two end sections they will intersect at an angle of 90°. The 
elbow shown at ^ is a four-piece elbow; the one shown at 5 is a 
six-piece elbow. At C is shown a 67J^° five-piece elbow. 

The two forms of elbows at A and B with the short throats 
are commonly used in stove-pipe work. The long throat used 
at C is more common in chutes, conveyor systems, etc., where the 
friction due to short bends is to be avoided. The middle sections 
of elbows are usually made equal to each other; the end sections 
are generally made half as long as the middle sections. 

The developments of the patterns for these three elbows are 
shown in Fig. 132. It will be sufficient to consider the construe- 



SHEET-METAL WORK 



137 



tion for the first elbow; the method is the same for the other two. 
The method shown here is in general use in the sheet-metal trade. 




a -^^ 





E (C) 

Fig. 132. — Developments of elbow sections. 

In developing the pattern for a section of the elbow shown in 
Fig. 131-A, a circle DEF should first be described to some definite 



138 ADVANCED SHOP DRAWING 

scale to represent a plan view of one of the end sections as in Fig. 
1S2-A. It will be noticed that in solving for the developments 
in the two examples, Fig. 132-5 and Fig. 132-C, only a half circle 
has been drawn. This is because the halves of the pattern 
are symmetrical, and, therefore, only a half pattern need be 
developed. Next, the circle DEF should be divided into a num- 
ber of equal parts. The right angle ahc should next be drawn 
above this circle to represent the 90° angle swept through by the 
elbow. With 6 as a center an arc adc should be described of 
any convenient radius ha; the angle ahc should be bisected by 
the line hd. The arc dc should be divided into a number of 
spaces one less than the number of sections in the elbow. For a 
four-pieced elbow this arc would be divided into three equal 
spaces; for a six-pieced elbow it would be divided into five equal 
spaces, etc. From the point of division nearest c a line should 
be drawn to the vertex h. This line represents the junction of 
the lower end section of the elbow with its mate, and the various 
points of division on the circle DEF should now be projected 
upon it. To the right, a base line MN should be laid out equal 
in length to the circumference of the pipe. It should be divided 
into a number of divisions equal to that into which the circle 
DEF was divided, and perpendiculars erected at the points of 
division. The various points in which the projectors of circle 
DEF intersect the line h-e may now be projected over to the 
corresponding base Hne elements in the development. A smooth 
curve passed through the series of points thus determined gives 
the developed outline of the intersection of two sections. 

This outline will be the same for any elbow of the same number 
of pieces, same diameter of pipe, and same angle swept through 
regardless of the throat radius of the elbow. Changing the throat 
radius will merely change the lengths of the line elements by 
equal amounts without in any manner affecting the development 
of the intersection. The length of the inside element, k-p, may 
now be pointed off with due allowance made for a joint with the 
straight pipe. It will be readily seen that the developed joutline 
for any middle section of pipe will be the same on both edges 
as the curve just determined. It will be evident from Fig. 132 
that the pattern for an elbow may be developed without making 
a complete drawing of the elbow in front elevation. 

Figure 133 shows how sections of an elbow may be cut from 
sheet-metal without waste if the job is not a particular one. It 



SHEET-METAL WORK 139 

will be evident, though, that when the patterns are cut this way, 
every alternate joint will be on the outside of the elbow and this 
will detract greatly from its appearance. 

68. Allowance for Thickness of Metal. — As stated in Article 61 
when metal of gage 20 or thinner is being used, no allowance need 
be made on the patterns for the thickness of metal. In the pre- 
vious discussion on sheet-metal work, no consideration was given 
to the thickness of metal. Before any pattern can be developed 




t Fig. 133. — Method of cutting patterns for elbows without waste of metal. 

by the draftsman, however, it is essential that he should have a 
knowledge of the properties of the material that he intends to 
use. The allowances for laps, lock seams, and wiring were 
referred to in Articles 61 and 62. One other important allow- 
ance must be made; namely, for bends in the material. For 
determining this allowance, the sheet-metal worker must rely 
partly on practical experience. A few general remarks will not 
be amiss, however. 

No allowance is made for bending, when working up sheet 
metal lighter than number 20 gage, unless extremely accurate 
work is desired, and this is rarely the case. 

When dealing with metal which is thicker than number 20 
gage, and exact inside or outside dimensions are to be maintained, 
careful attention must be given to the thickness of the metal. 
In considering the cylinder shown in Fig. 134, which is made 
from metal of considerable thickness, it will be evident that the 
length of metal required to form this cylinder will be equal to the 
circumference of the center line circle, that is, equal to the 
length of the center line of the metal. The various parts may be 
designated as follows: 

D = the diameter of the center line 
Di = the inside diameter 
D2 = the outside diameter 
t = the thickness of metal 



140 



ADVANCED SHOP DRAWING 



By reference to Fig. 134, it will be seen that the following equa- 
tions may be written, 

D = Di + t 

D = D2- t 

The developed length of metal necessary, when an exact inside 
diameter is to be maintained, may be readily determined from 
the first equation. From the second equation, the length of 
metal necessary to preserve an exact outside diameter may be 




Fig. 134. — Sheet metal cylinder constructed of thick metal. 

computed. As a general rule, the first equation is the one more 
commonly used; that is, an exact inside diameter is to be main- 
tained. In such cases, shopmen compute the inside circumfer- 
ence and add an allowance for forming the curve. It will be 
seen that for a complete circle the length of the center line will 
be 3.1416 X D and that 

3.1416 X D = 3.1416 X Di - 3.1416^ 

In making a simple bend, the metal will stretch on the outside 
and shorten on the inside of the curve, and the original length 
of the sheet will be at the center line of the metal or very close 
to it. Consequently, the pattern should follow the center line 
of the stock, and, if the dimensions of the inside of a curve are 
available, "3.1416 X the thickness" as an allowance for bending 
should be added. This is more often used as S^'jt, since 3J7 or 
2% is near enough to 3.1416. 



SHEET-METAL WORK 141 

The method of working the metal in making the bend may alter 
somewhat the necessary allowance. If the metal is hammered 
into shape, it will stretch and the allowance need not be so great. 
In some shops, an allowance anywhere from three to seven times 
the thickness of metal is made and the sm^plus metal removed 
after bending. 

It should be clearly understood that what has been said re- 
garding allowances in the preceding paragraph applies to com- 
plete cylinders. If the bent portion encloses only half of a 
cylinder, the allowance will be only half of that required for a 
complete cylinder, etc. For a quarter turn or 90° bend, the 
allowance should be one-fourth that for a complete cylinder. 

In the case of patterns of irregular outline, allowance must be 
made before the pattern is developed so that the metal may 
distribute itself evenly while being shaped. 

Square and angular bends are the kind most commonly encoun- 
tered by the shopman. When metal of any considerable thick- 
ness is used, its thickness may have an appreciable effect where 
accurate inside or outside dimensions are to be obtained. Where 
it is impossible to make sharp bends, either due to the thickness 
or the stiffness of the metal, the drawing must show" the corners 
rounded in the form which the metal will assume. The allow- 
ance to be made for such bends will be largely determined by the 
practical experience of the shopman. If the draftsman desires 
accuracy for such cases, he w^ill find it well to take a sheet of the 
specified metal and form it into the desired shape. In doing so 
he will know whether he has to obtain accuracy in the inside or 
outside measurement or on the center line. The length of the 
resulting center line of the section may then be readily deter- 
mined for plotting the development. A test like this is the only 
safe and definite method that can be recommended for all cases; 
the outline of the drawing should always follow the center line 
of the material. 

No definite rules can be given that will apply in all cases. 
Different flanging, bending, and forming machines take up differ- 
ent amounts of material. The experience of the workman must 
furnish the needed guidance. It has been evident in all allow- 
ances which have been made for seams in the previous problems 
in sheet-metal work, that the dirnensions for the seams were not 
noted. In working up heavier sheet metals, a great many of 
the details must be left to the shopman as these details are af- 



142 



ADVANCED SHOP DRAWING 



f ected considerably by the individual practice of the shopman and 
the machinery with which he has to work. However, allowances 
for sheet metals thicker than number 20 gage should be shown on 
the drawing. 

Problem 21 

Make a development, by triangulation, of the transition piece shown in 
Fig. 135. Dimension the development completely so that the man in the 




Fig. 135. 

shop could make a pattern from it. Allow material on one edge for riveting. 
A transition piece is used to connect openings of different sizes as in pipe 
work. This one has one base 4 ft. in. square, and the other base is 2 ft. 
in. square. The two bases are spaced 3 ft. in. apart. 



Problem 22 

Develop a half pattern for the gusset sheet A shown in Fig. 136. 

Longitudinal and cross-section views of this boiler are shown in Fig. 137. 
The part for which the pattern is to be developed is that which lies between 
the lines CD and ED in the cross-section view, Fig. 137. 

This boiler is made of sheet steel %" thick; 3-in. seams are provided 
for riveting. It should be noticed how the slope of the side seam B is de- 
termined by the horizontal center lines of the cylindrical parts. The bot- 
tom parts of the three sections of the boiler are horizontal. 



SHEET-METAL WORK 



143 



This problem is most readily solved by triangulation as was explained 
in Fig. 130. In this case, however, due to both bases being circular, it will 
simplify the work to divide both bases into the same number of equal parts. 

In dealing with metal of greater thickness than number 20 gage, it is 
always necessary to develop the pattern for the center line of the metal. 




Fig. 136. 

The circular bases of the center lines of this gusset sheet are 41% in. and 
36^^ in. in diameter, respectively. The length of the quarter-circumfer- 
ence of each base should be computed, plotted as a straight line, and divided 
into the same number of parts as the corresponding section of the circular 
base The length of each part will then be the distance between the points 





MATeRlAL-SHEETSTEEL | THICK 

Fig. 137. 

of division on the circular base, and is the distance that is to be used as a 
radius in determining the development by triangulation. 

The true lengths of the lines drawn between the points of division on the 
two bases must next be determined. 

These constructions give all the data necessary for proceeding with the 
development of the half pattern. 



INDEX 



Acme threads, 4 
Addendum circle, 19 
bevel gear, 33 
spur gear, 19 
Annular gears, 25 
Assembly drawings, 1 

B 

Bevel gears, 31 

Bevel gears, layout, 31 

Bill of material, 4 

Black prints, 13 

Blue prints, 12 
exposure, 12 
machines, 12 
mounting, 13 
paper, 12 
washing, 12 



Cabinet drawings, 53 

angles of axes, 54 

circles, 56 
Circles, addendum, 19 

cabinet drawing, 56 

clearance, spur gear, 21 

dedendum, 21 

isometric, 49 

pitch, 15 

root, 21 

D 

Dedendum circle, 21 
Detail drawings, 6 
Details, 6 

space given to, 8 
Detail sheets, 2, 6 



Development, by triangulation, 132 

cones, 117 

cylinders, 115 

elbows, 136 

prisms, 124 

pyramids, 125 
Diagram drawing, 1 



E 



Electrical drawing, 86 
bell circuits, 87 
symbols, 86 

three-wire circuits, 90, 93 
two-wire circuits, 89 
wire sizes, 87 
wiring diagrams, 93 

Erection drawings, 1 



G 



Gear drawings, spur, 25 
keys and keyways, 28 
length of hub, 27 
outside diameter, 26 
pitch diameter, 26 
root diameter, 26 
thickness of arms, 27 
thickness of rim, 27 
tooth outlines, 28 
width of arms, 27 
width of face, 28 

Gears, 15 

annular, 25 
bevel, 31 
herringbone, 41 
spiral, 41 
spur, 15 
stepped, 39 
twisted, 39 

Gears, bevel, 31 
addendum, 33 
145 



146 



INDEX 



Gears, bevel, backing, 33 

cutting angles, 35 

depth of teeth, 33 

edge angles, 35 

face angles, 34 

outside diameter, 34 

pitch angles, 34 

thickness of rim, 33 
Gears, spur, 15 

addendum circle, 19 

calculations, 17 

clearance circle, 21 

dedendum circle, 21 

drawings, 25 

velocity ratio, 23 
Gear tables, 20, 22 
General assembly drawings, 2 



H 



Herringbone gears, 41 



Intersections, 116 

cone and plane, 116 
plane and prism, 123 
two cyUnders, 127 
two prisms, 126 

Isometric drawings, 47 
arcs, 50 
axes, 48 
circles, 49 



Part assembly drawing, 1 
Patent office drawings, 67 

application, 67 

drawing, 68 

examination, 68 
Piping, 100 

dimensions, table of, 101 

drawings, 104 

fittings, cast iron, 102 

fittings, malleable, 103 

isometric plans, 108 

kinds of, 100 

sizes, 100 

symbols, 103 

table symbols, 112 

thread, 101 

two-pipe system, 105 

typical connections, 108 
Pitch, 17 

circles, 15 

circular, 18 

diameter, 17 

diametral, 17 

spiral gears, 42 

twisted gears, 40 

worm gears, 38 

R 

Rack and pinion, 25 
Root circles, 21 



Legend, 8 

Line shading, 60 

brilliant line, 61 

cone, 63 

cylinder, 61 

flat and graded tints, 62 

hollow cylinder, 62 

sphere, 63 



O 



Outline assembly drawing, 1 



S 



Scale, 8 

Shaded drawings, 57 

Shade lines, 57 

rules of, 58 
Sheet metal drafting, 114 

allowance for thickness, 139 

curves and circles, 115 

development by triangulation, 
132 

elbows, 136 

intersections, 116, 123 



INDEX 



147 



Sheet metal drafting, materials, 
118 

principles, 114 

seams, 120 

table, copper, 120 

table for iron and steel, 118 

triangulation, 132 

true length of line, 132 

wiring edges, 120 
Special gears, 25, 39 

annular gears, 25 

rack and pinion, 25 
Spiral gears, 41 

dimensions, 44 

number of teeth of, 46 

pitches for, 42 

size of blanks for, 43 

velocity ratio, 42 
Spur gears, 15 
Structural drawing, 75 

assembly shop, 84 

beam shop, 84 

dimensions, 78 

drafting department, 75 

estimating department, 75 

examples of, 79 

lettering, 78 

line conventions, 78 

riveting conventions, 76 

shop bills, 76 

symbols, 77 

templet shop, 83 

yard, 84 
Symbols, 77 

electrical, 86 

piping, 103 

structural, 77 

table of piping, 112 



Tables, cast-iron fittings, 105 

fitting symbols, 112 

keys and keyways, 29 

malleable iron fittings, 106 

sheet copper, 120 

sheet iron and steel, 118 

standard steel and wrought iron 
pipe, 101 

tooth gears, circular pitch, 22 

tooth gears, diametral pitch, 20 
Threads, Acme, 4 
Titles, 9 
Tracing, 11 

inking in, 12 

order of procedure of, 11 

preparing cloth, 11 
Triangulation, 132 
True length of line, 132 
Twisted gears, 39 

tooth angle, 41 

velocity ratio, 41 



V 



Vandykes, 13 

Velocity ratio, spiral gears, 42 

spur gears, 23 

twisted gears, 41 

worm and worm wheel, 36 

W 

Worm and worm wheel, 36 
pitch, 38 

shop drawing of, 38 
velocity ratio, 36 



